GIFT OF Civil Eng. UNIVERSITY . . -, - , ..'< .r jri'-' '" BERKEUEY. ENGINEERING LIBRARY OF WILLIAM B. STOREY A GRADUATE OF THE COLLEGE OF MECHANICS CLASS OF 1881 PRESENTED TO THE UNIVERSITY 1922 MODERN LOCOMOTIVE CONSTRUCTION BY J. G. A. MEYER ASSOCIATE EDITOR OF THE " AMERICAN MACHINIST ; " MEMBER AMERICAN SOCIETY MECHANICAL ENGINEERS ; FORMERLY CHIEF DRAFTSMAN AT THE GRANT LOCOMOTIVE WORKS Illustrated NEW YORK JOHN WILEY AND SONS 53 EAST TENTH STREET 1892 IV I'll E FACE. The principles upon which the methods of construction are based are generally given, so as to enable any one who designs with the necessary regard to theory to make modifications to suit his own ideas. In writing the original articles I have aimed to make each one as complete as possible. This necessarily required a few repetitions, which were allowed to remain in this book, as it was thought such a course would make the book more convenient for reference. My thanks are due to Mr. P. Arnot, Supt. of the Grant Locomotive Works, when these works were located at Paterson, N. J. ; to Mr. John Headden, formerly Supt. of the Roger Locomotive Works ; Mr. D. Shirrell, draftsman at the Richmond Locomo- tive Works ; and other friends, for valuable suggestions and assistance in the prepara- tion of this work. I am also indebted to Mr. Theo. N. Ely, General Supt. of Motive Power, Pennsylvania R. R. ; the Grant Locomotive Works ; the Cooke Locomotive Works, of Paterson, N. J. ; the Rogers Locomotive Works, of Paterson, N. J. ; the Rhode Island Locomotive Works, Providence, R. I. ; the Baldwin Works, Philadelphia, Pa. ; the Richmond Locomotive and Machine Works, Richmond, Va. ; and Mr. A. J. Pitkins, Supt. of the Schenectady Locomotive Works, Schenectady, N. Y., for kindly furnishing me with drawings and data. PATERSON, N. J., September, 1892. CONTENTS. CHAPTER I. PAOE INTRODUCTORY REMARKS. CLASSIFICATION OP LOCOMOTIVES. TRAIN RESISTANCE. TRACTIVE POWER. WEIGHT OF ENGINES 1 CHAPTER II. CONSTRUCTION OF CYLINDERS. STEAM PIPES. SLIDE VALVES 20 CHAPTER III. VALVE GEAR. CONSTRUCTION OF LINKS 74 CHAPTER IV. PISTONS. CROSSHEADS. SLIDES. STUFFING BOXES 138 CHAPTER V. FRAMES AND PEDESTALS. AXLE BOXES 182 CHAPTER VI. DRIVING AXLES. DRIVING WHEELS. COUNTERBALANCE 214 CHAPTER VII. MAIN-RODS. SIDE-RODS. CRANK-PINS 267 CHAPTER VIII. THROTTLE PIPES. THROTTLE VALVK GEAR. SAFETY VALVES. WHISTLE. PI-.MI-S. CHECK- VALVES 343 CHAPTER IX. SPRING GEAR AND SPRINGS 400 CHAPTER X. BOILERS. GRATE SURFACE. HEATI MI SURFACE. RIVETED JOINTS. EXTENSION FUONTS... 417 v i CONTEXTS. CHAPTER XI. |>A ,. E ASH-PANS. SMOKE-STACKS. EXHAUST-PIPES -101 CHAPTER XII. SAND-BOXES. BELLS. PILOTS. ENGINE-BRACES 510 CHAPTER XIII. ENGINE TRUCKS 535 CHAPTER XIV. OIL-CUPS. VALVES. COCKS. INJECTOR 552 CHAPTER XV. TENDERS. TENDER-TRUCKS 563 CHAPTER XVI. USEFUL RULES, FORMULAS, AND DATA 595 CHAPTER XVII. COMPOUND LOCOMOTIVES 617 MODERN LOCOMOTIVE CONSTRUCTION. CHAPTER I. INTRODUCTORY REMARKS. CLASSIFICATION OF LOCOMOTIVES. TRAIN RESIST- ANCE. TRACTIVE POWER. WEIGHT OF ENGINES. 1. Ill late yours a change in the management and treatment of the locomotive lias taken place on most of our principal railroads. This change necessarily caused, also, a change in the construction of the locomotive, besides other improvements that have been added from time to time. "2. It is the writer's intention to give in these chapters a general description of the principal parts of the modern locomotive, illustrated by good and correct drawings, and indicate the improvements that have been added. Since all the illustrations represent separate parts of the modern locomotive, and since some of them will be arranged in a tabular form (an arrangement the writer has not seen in any book, and consequently believes it to be new), we trust that these illustrations will be appreciated by the professional designer, and by the young designer in particular. 3. In order to make the reading of these papers profitable to the mechanic, we will, in connection with tin; illustrations, give rules relating to the proportioning of tin- parts in as plain and simple language as we can command, so that any one engaged in the building and running of tin- locomotive may easily understand these rules. \\Y also hope that the description of the locomotive, which is almost inseparable from a subject presented in a manner as we propose to do, will prove interesting to the ordinary reader. Should any of our professional friends pronounce the* rules given as something superfluous, because they may be found in the many excellent books already published, or should .-my of our friends find fault with the practical method of treating this subject, we would kindly remind them that these chapters are intended fora large class of readers for the mechanic and engineer in particular and not fora favored few. ,' *'."' t i .'. ' '. vU : "'', : - I,' < * l' MODERX LOCOMO Tl 1 7v f 'O.Y.S Tit rt ' TION. 4. When a comparison is made between the locomotives built recently and the locomotives in use about ten or twelve years ago, a change in their construction and appearance will be noticed. This change is due to the desire of railroad managers to reduce the cost of transportation of passengers and freight, and to a great extent this desire has been realized. 5. In former times it has been the custom to place an engine in the hands of one engineer, and whenever the engine was attached to a train this same engineer had his hand on the throttle lever. When the trip was completed, the engine was carefully housed and cleaned, and, so to speak, was put to rest. In fact, we once heard an engineer say (and we have reason to believe that he was in earnest) that engines needed rest as well as engineers, because he noticed that his engine never worked as well when Hearing the end of a trip as it did when starting. If this engineer is still among the living, he must either have changed his opinion or stepped off the footboard to stay off. The trips also were comparatively short, and generally the trains comparatively light. Indeed, when we carefully consider the management of the locomotive and the treatment it received in former times, we might almost conclude that the locomotive was looked upon as a delicate piece of machinery that needed extraordinary care to keep it in good working order. But now, mark the change of treatment of the engine that has taken place on some of our best railroads. Notice, for instance, on these roads the modern freight locomotive as it starts off with as heavy a train as it can possibly haul on a trip of great length, the engineers relieving each other at designated stations, instead of one engineer having charge of the engine during the whole trip, as in former times; notice also the scanty accommodations, if any, for cleaning or housing the engine when the trip is completed ; the short time the engine is allowed to stand still after it has been examined and found to be in good working order ; the heavy train it must haul on the homeward journey, run by any engineer that is competent to run an engine ; and when the starting point has been reached, no time is lost in coupling it to another train, and thus it is kept running almost continually in all kinds of weather. Compare this treatment to the former and the change must become apparent. G. The passenger engines are sometimes subjected to the same severe treatment, but generally an engine is placed in the charge of only two engineers, one of these running the engine during one trip, and the other having charge of it during the next trip, and so relieving each other alternately. 7. Allowing different engineers to run the same engine has this advantage, namely : that only competent engineers can hold their positions, because after a competent engineer has once shown what the engine can do, the other engineers must make the engine perform a like amount of work in the same time, or give good reasons for not doing so. Here then we perceive that no incompetency is admissible. 8. The passenger trains are also heavier now than in former times, and the trips longer. Generally speaking, all engines are now required to do more work than formerly. Engines placed in such severe service must naturally be strong, powerful and durable, well put together, bolt holes reamed, bolts turned and fitted, and driven in tightly. In the modern locomotive the boiler is larger than in former practice, the frames and cylinders are heavier, and generally all working parts are made stronger. M<H>Kl;\ l.ni-n.wnr/l'K CONSTRUCTION. 3 0. Ill the appearance and outside finish of the engine we also notice a decided change. For instance, (lie landscape paintings and pictures of birds and horses on the side ot' the tender, have of late disappeared, and the tanks are plainly painted with good paint, and well varnished. This is, in the writer's opinion, as it should be, because pictures on the side of the tank seem to him to be out of place. A tender is made for the purpose of carrying water and fuel, and is ill adapted for a picture-gallery. The brass finish on the engine and fancy ornaments, such as eagles, etc., are also things of the past, because these require too much time and expense to keep clean and in good condition. From these remarks the reader must not conclude that in former times the engines had a better and more pleasing appearance. This is not the case, because years of experience have exposed faulty constructions in former locomotives, which h;,ve been corrected and otherwise improved in the modern engine, and since correct construc- tion and distribution of metal must always improve the appearance of a machine, we conclude that our American locomotives as now built (although by no means perfect) possess elegance in form, compactness in the arrangement of the different pieces of mechanism, and gracefulness in movement. CLASSIFICATION OF LOCOMOTIVES. 10. We may divide the different kinds of locomotives into two distinct classes; in one class we may place the ordinary passenger and freight locomotive, and in the other the switching engine and other locomotives designed for some special service. At present we will consider only the first class, namely, the passenger anu freight locomotives. These engines are again divided into four different classes, namely : 1st, the eight-wheeled engine; 2d, the Mogul engine; 3d, the ten-wheeled engine; 4th, the consolidation engine. An eight-wheeled engine, sometimes called the American locomotive, because this design was first brought out in this country and used here more than elsewhere, is an engine that has four driving wheels and four truck wheels, as shown in Fig. 1. On some roads the eight-wheeled engine is used for both passenger and freight service, 1ml generally it is recognized as the passenger engine. A Mogul engine is an engine that has six driving wheels and two truck wheels, as shown in Fig. 2. These engines arc used principally for freight service; occasionally they are used for passenger service, but generally they are recognized as freight engines. A ten-wheeled engine is one that has six driving wheels and four truck wheels, as shown in Fig. 3. Ten-wheeled engines are used for fast freight service, for hauling heavy passenger trains, or for a mixed traffic. A consolidation engine is an engine that has eight driving wheels and two truck wheels, as shown in Fig. 4. These engines are used for heavy freight service on roads having steep grades. Now, notice the eight- wheeled engine and the Mogul engine; each one has eight wheels. In the passenger engine four wheels of the whole number are driving wheels, and in the Mogul engine six wheels of the whole number are driving wheels. Again, notice the ten-wl led engine and the consolidation engine; each one has Fifj.l EIG II T- WHEELED EX 'G INK Fig. 2 Jliffid-WlicelRase Total Wheel- Base -Itiyltl- Wheel- llaxr Total Whvvl-Itase COKSOLIDAXIOX ENGINE <-<>.\sri;n n<>\. ten wheels. In th<- ten-wheeled engine six wheels of I lie whole number are driving wlieels, ;IIK! lii the consolidation eight wheels of the whole number ai*e driving wheels. WHEEL BASE. 11. The rigid wheel base of any engine is the distance from the center of rear to the center of the front driving wheel, plainly shown in figures. The total wheel base of any engine is the whole distance from the center of the rear driving wheel to the center of the front truck wheel, also plainly shown in figures. DATA REQUIRED. 12. Before we can decide what type of a locomotive to adopt, and before we can determine the dimensions of this engine, we must know the following particulars: 1st, the total weight of the train that is, the combined weight of the load and cars; 2d, the speed of train; 3d, the grades and curves of the road on which the engine is to run ; 4th, gauge of track that is, the exact distance between the rails; 5th, the weight on the drivers that the rails of the road can hear; (5th, kind of fuel to be used ; 7th, kind and height of couplings of cars; 8th, limitations, if any, in width, height, length, etc., by tunnels, overhead bridges, turn-tables, etc. For the sake of simplicity, let us first find the type and the dimensions of a locomotive cajiable of hauling a train of given weight on a straight and level track, leaving the speed and all other particulars out of the question. TRAIN RESISTANCE. 13. The principal resistance which a locomotive must overcome in slowly hauling a I rain over a straight and level road, is rolling and axle friction. Hence the resistance to motion of a train, or the train resistance, is simply rolling and axle friction combined. But it must be remembered that when a train is to run fast, or against strong winds, other forces must be overcome. By rolling friction is meant the resistance to motion that takes place where the circumference of the car wheel comes in contact with the rail. Axle friction is the resistance to motion that takes place between the axle journal and its bearing. 14. An ordinary train, composed of cars whose wheels are, say, from 28 inches to ''>- inches in diameter, and having journals, say, from .'! inches to 3J inches in diame- ter, will require a force of 7 pounds for every ton of 2,000 pounds to move it. Thus, for instance, if the total weight of the cars and the load is 1,000 tons, we have 1,000 x 74 = 7,500 pounds ; this means that a train of 1,000 tons requires a force of 7,500 pounds to move it, or, in other words, it requires a force of 7,500 pounds to overcome the combined rolling and axle friction. On some roads it may require only <> pounds for every ton, and on other roads it may require !) pounds to move a ton weight. This difference is caused by the degree of smoothness and irregularities of the rails, the different proportions of the wheels and journals, the kind of springs under the cars, the kind and quantity of oil used. Fig. 5 6 MODERN LOCOMOTIVE COXSTRUCTION. and other minor conditions. We believe that 1\ pounds per ton will bo suitable for the average railroads, and this figure we shall hereafter adopt in all our calculations in which speed and the grade is not taken into account. 15. The amount of the combined rolling and axle friction of a train, which a loco- motive must overcome, can be found by several practical methods. For instance: Assume that one end of a rope is attached to a car, and the other end, c, of rope passed over pulley, b, as shown in Fig. 5. The bearings of this pulley are supposed to be firmly fastened to the track, and the height and position of the pulley being such that portion a // of the rope will be parallel to the rail; then a weight fastened to the end, c, of the rope, and sufficiently heavy to move the car, and no more, will be the force in pounds necessary to move it, or, in other words, this weight will be the force neces- sary to overcome the combined rolling and axle friction. Hence, if the weight of this car is 20 tons, we may expect to find that a weight from 120 to 180 pounds will move it, this dif- ference of weight being caused by the conditions of the rail, etc., as before explained. Now, the mean between 120 and 180 is 150 pounds to move 20 tons, which is equiva- lent to 7 pounds per ton. Again, we may try another method. Instead of placing a coiipling-bar between the tender and cars, let us couple these by an instrument capable of measuring a force. Such an instrument is called a dynamometer. There are different kinds of dyna- mometers, the simplest being a spring balance, sufficiently strong to withstand the pull, and yet elastic enough to indicate correctly the force in pounds exerted by the engine in pulling the train. Although the spring balance is not always the best instru- ment to use for this purpose, and is adapted only for moderate forces, we draw atten- tion to it because its action is familiar to the reader, and probably best understood. Now suppose a correct spring balance is placed between the tender and a train whose weight is 1,000 tons, then, as soon as the engine commences to pull and move the train, our spring balance will show a force from 6,000 to 9,000 pounds. The mean between 0,000 and 9,000 pounds is 7,500 pounds, which is again equivalent to 7 pounds per ton. We may also determine by observation the force necessary to move the train. It has been found that railroad cars, with wheels and axles as before described, will begin to roll down a grade when it is as steep as from 16 to 24 feet per mile. Of course, this difference is caused by the condition of the track and other considerations before men- tioned. Let the length of the line a c, Fig. 6, represent a mile, and the length I c the rise of the grade, namely, 16 feet. In that branch of science called mechanics it has been proved that the force necessary to overcome friction is as much smaller than the weight * of the cars as the length of the line I c is shorter than the length of the line a c. * Instead of the word "weight," we should have said "pressure," because the weight and pressure arc equal only on a level track, and not on a grade; Imt in this particular case, the difference being so small, we have, for The' sake of simplicity, used the word "weight." How to find this difference will be explained hereafter. M<)l>l-:i:\ l.tti-tt.MoTII'K CONSTRUCTION. 7 Now, the line n < represents one mile, or .">,2SO feet, .-mil (he line It c 1G feet; dividing r>,2SO ft 'ft liy It! t'cft, \vf liavt- ' "'. = :!:>(), that is, the line a c is 330 times longer than tin- line l> c, hfiicf the weight of the cars will be 330 times greater than the force ''000 necessary to overcome friction. Now, there are 12,000 pounds in a ton, hence - rr = 6.06. oou This nn'.nis that it requires (i pounds per ton to move the train. If we assume the grade to lie 24 feet in a mile when the cars begin to roll down the grade, then the line 5280 It r, Fig. (i, will he '24 feet long, and ~ = 220, that is, the line n c is 220 times longer &* ''000 than the line \> r, therefore ~^-r J) pounds per ton to move the train, or to overcome rolling and axle friction; the mean between 6 and 9 pounds is 7 pounds, as before. From this we may establish a rule for finding the force nee- Fiy.H essary to overcome the train resistance, the speed not being taken into consideration. RULE 1. Multiply the weight of the train in tons (of 2,000 pounds) by 7; the answer will be (lie force in pounds necessary to overcome the train resistance. If to this we add th" resistance of the lender and its load, also the force necessary to move the engine itself, we then know the force an engine must exert to haul the total load. For all practical purposes we may assume that 7 A pounds per ton is not only suffi- cient to move the train, but also includes the force necessary to move the engine and overcome the friction of its machinery, hence no separate calculation for this is necessary. The resistance of the tender is found by Rule 1 that is, multiply the weight in tons of the tender and its load by 7J, and the answer will be the force in pounds re- quired t<> overcome this resistance. Or, still simpler, add the weight of the tender and its load to the weight of the train and multiply the sum by 7i. Thus, K\AMi'LE 1. The weight of a train is 1,200 tons, and the weight of the tender 2(1 tons ; find the force in pounds necessary to haul this train ; 1,200 4- 20 = 1,220 tons, 1,221) x 7i = !),!")() pounds, hence the engine must be capable of exerting a total pulling force of !),!.")() pounds. ADHESION. 16. The effort to haul a train which a locomotive can exert is limited by the adhesion between the driving wheels and the rails. This adhesion is simply friction between the driving wheels ami rails acting so as to prevent slipping. If, for instance, the train resistance exceeds the adhesion, the driving wheels will slip, or, in other words, turn round without advancing. The adhesion depends upon the weight placed on the drivers. When the rails are dry and in comparatively good condition, we may assume that the adhesive force is equal to 1 -of the weight on the drivers. Thus, for instance, if the weight on the drivers is 40,000 pounds, the adhesive force will be S,000 pounds. This adhesive force enables an engine to pull a train, and must not be less than the train resistance. g MODERN LOCOMOTIVE CONSTRUCTION. When the rails are wet, muddy, or greasy, this adhesive force will be considerably less, and snowy or frosty weather will also reduce the adhesion. In the following calculations we shall consider the track to be in good condition, and therefore shall assume the adhesion to be equal to .' of the weight on the drivers. If the condition of the track is not known, the writer believes that the adoption of -,V of the weight on the drivers for the adhesion will not lead to disappointment as often as when \ is adopted. WEIGHT ON DRIVERS. NUMBER OF DRIVING WHEELS. 17. From the foregoing remarks we have learned that when the weight of the train and tender is known we can find the train resistance ; also, that the adhesion must at least be equal to the train resistance, and since the adhesion is equal to i of the weight on the driving wheels, we multiply the train resistance or the adhesion by 5, the prod- uct will be the total weight on all the drivers. EXAMPLE 2. In Example 1 we found the train resistance to be 9,150 pounds ; what must be the total weight on the driving wheels? 9,150 x 5 = 45,750 pounds, hence the total weight in all the drivers will be 45,750 pounds. On some roads heavy rails are used, on other roads lighter rails are adopted. The heavy rails can, of course, bear a greater weight on the drivers than the lighter rails, therefore, before we can find the number of drivers under an engine, we must know the weight that the rails can bear. 18. When an engine is running on light rails about 30 pounds per yard we may place 4,000 pounds on each driver ; and when an engine is running on heavy rails we may place 15,000 pounds on each driver. In late years the tendency has been to crowd all the weight on the drivers that can possibly be placed on them, so that now on some roads more than 15,000 pounds ai-e placed on a driver. But there must be a limit to this weight, because when too much weight is placed on the drivers, either the tires, the rails, or both, will be injured. The exact amount of weight that can be placed on the drivers has not yet been satisfactorily established, but we believe that the fore- going figures, namely, 4,000 to 15,000 pounds on each driver, according to size of rail, may be safely adopted. From these remarks it must be evident that before we can decide which of these two figures we can use, or what amount of weight between these two limits we may adopt, we must know the material of which the rails are made, and the weight of rail per yard, that is, their form and size. Of course, we are now alluding only to rails for ordinary passenger and freight engines on roads of 3 feet gauge, or other roads up to 4' 8" gauge, and we do not include the rails for mining engines, plantation engines, or wooden rails. Another important fact that we must not overlook is the weight the bridges can bear, because the rails may be suitable for a heavy load, and the bridges may not be so. 19. If, then, we know the weight that can be safely placed on each driver, we can find the number of drivers to be placed under an engine by : RULE 2. Divide the weight that must be placed on all the drivers by the weight that can be safely placed on one driver, and the quotient will be the number of driving wheels required. K .'!. The .greatest weight <>n each driver that the rails of a given road can hear is 1(1,1100 pounds, and the weight necessary on all the drivers to haul the train is 40,000; how many driving wheels must be placed under the engine! According to 1 1 |, w w \ the rule we have - = 4, hence the number of drivers will be four. If the necessary 1 0( M K) weight on all the drivers had been (iO,000 pounds, we then would have to place six drivers under the engine so as not to exceed 10,000 pounds on each. DIAMETERS OF DRIVING WHEELS. 20. The diameter of the driving wheels under an engine will, to a great extent, depend upon tin- speed of the locomotive. Driving wheels of large diameter are neces- sary for fast speeds; and, on the other hand, driving wheels for heavy freight engines must necessarily be comparatively small in diameter. There are several causes which Fig. 7 will place a limit to the diameter of a driving wheel in either direction. We will name two: The diameter must not be too large, because, if it is, the engines will stand too high. The diameter must not be too small, because, if it is, difficulty will be experi- enced in getting steam out of the cylinder on account of the high piston speed which may be necessary for the required speed of train. Between these two limits no exact rule for finding the diameter of a driving wheel can be given. The following tables will greatly aid us in determining the diameters of these wheels. These tables show the diameters of driving wheels for the different classes of engines, such as are gener- ally adopted by builders and master mechanics, and giving good satisfaction. In these tables we see that, for an eight-wheeled engine with cylinders 10" in diameter and 20" stroke, we may use driving wheels 45" diameter, or larger, up to 51" diameter; or, if it is an eight-wheeled engine with 17"x24" cylinders, we may adopt driving wheels (i()" diameter, or larger, up to (50". Of course, these limits of driving wheels for the different classes of engines are not absolute. We may change, and, indeed, may be compelled to change, these diameters to suit some particular service. But it must be remembered that when the number of revolutions of the driving wheel per mile are given, then the diameter of the driver is not a matter of choice, but must be found accurately l, v calculation, which is an easy matter. Thus, for instance, the number of revolutions of the driving wheel per mile is :!:!<>: what must be the diameter of the wheel .' One mile is equal to 5,2S() feet; then dividing 5,280 by the 5* 'SO number of revolutions, namely, :>:!(>, we have - - = 15.71. This quotient is the number of feet in the circumference of the wheel. Now, if we refer to a table of circumferences, we find that the diameter of a circle, whose circumference is 15.71 feet, is equal to 5 feet. If such a table is not at hand, then divide the 15.71 feet by 10 MODERN LOCOMOTIVE CONSTRUCTION. 3.1416, because the circumference is always 3.141 G times greater than the diameter, and the quotient in this case will be 5 feet, which is the diameter of the wheel. TABLES SHOWING THE DIAMETERS OP DRIVING WHEELS AS GENERALLY ADOPTED FOR DIF- FERENT CLASSES AND SIZES OF LOCOMOTIVES. ALL DIMENSIONS IN INCHES. TABLE 1. EIGHT-WHEELED ENGINES. TABLE 2. MOGUL ENGINES. TABLE 3. TEN-WHEELED ENGINES. TABLE 4. CONSOLIDATION ENGINES. Cylinder?. Diameter. Stroke. Driving Wheels. Diameter. Cylinders. Diameter Stroke. Driving \Vh<-rle. Diameter. Cylinders. Diameter. Stroke. Driving Wheels. Di:i meter. Cylinders. Diumeter. Siroke. Driving Wheels. Diameter. Column 1. Column a. Column ]. Column 2. Column 1. Column 2. Column 1. Column 2. 10 x 20 11 x 22 12 x 22 13 x 22 14 x 24 15 x 24 16 x 24 17 x 24 18 x 24 45 to 51 45 to 51 48 to 54 49 to 57 55 to 61 55 to 66 58 to 66 60 to 66 61 to 66 11 x 16 12 x 18 13 x 18 14 x 20 15 x 22 16 x 24 17 x 24 18 x 24 19 x 24 35 to 40 36 to 41 37 to 42 39 to 43 42 to 47 45 to 51 49 to 54 51 to 56 54 to 60 For Narrow Gauge. t 3' 0" to 3' 0" 12 x 18 13 x 18 14 x 20 15 x 22 16 x 24 17 x 24 18 x 24 19 x 24 39 to 43 41 to 45 43 to 47 45 to 50 48 to 54 51 to 56 51 to 56 54 to 60 ] 14 x 16 (15 x 18 :;ii to 38 36 to 38 For 4' 8i" Gauge. ) 20 x 24 48 to 50 \ 22 x 24 50 to 52 The reason why 5,280 is divided by the number of revolutions per mile is simple, and yet it is not so generally understood among mechanics as we might expect, there- fore the following explanation is offered : Let the line a &, Fig. 7, represent one mile that is, 5,280 feet and c the center of the wheel when it stands at the end, a, of the line a ft, as shown in the figure. Care- fully rolling this wheel without slipping along the line a b until it has completed one revolution, or made one complete turn, the number of feet that it has traveled along the line a b is equal to the number of feet in its circumference. Now, if this wheel is 5 feet in diameter, its circumference will be 15.71 feet, nearly, and the distance from the center c to the center co, which is equal to the distance that it has traveled along the line a b, will be 15.71 feet. Again, if we continue rolling this wheel along the line a b until it has made another complete turn, then its center will be at cs, and the distance that the wheel has traveled from the point a along the line a b will be equal to the distance between the first center c and c* that is, 31.42 feet which is obtained by multiplying 15.71 x 2 ; and so on for every revolution it will travel 15.71 feet further ; and therefore, if we divide the length of the line a b, or one mile, by the circumference of a wheel, which is, in this case, 15.71 feet, we will know the number of revolutions that it must make to travel from a to b. And conversely, if we know the number of revolu- tions per mile, we divide the number of feet in a mile, or, as in our example, the length of the line a b by the number of revolutions, and the quotient will lie the circumference of the wheel, aud dividing this circumference by 3.1410, will give its diameter. Tli.UTIVF. POWER. DIAMETER OF CYLINDERS. Jl. \\'c now come tn the consideration of the size of cylinders necessary to turn the driving wheels. Neglecting the friction of the niiicliinciy, we may say that the cylinders with a given steam pressure must be large enough to almost slip the wheels, that is, to turn the wheels without advancing on the rails, when the engine is attached to the heaviest train that it was designed to haul. Or, in other words, if a certain amount of weight is placed on the drivers to haul a given train, we must design our cylinders so that a sullicieut power can be obtained to turn the wheels, and not more and not less, when the engine is attached to this train. This power which is necessary to turn the driving \vl Is under the above conditions is called the " tractive power"of a locomotive. If the cylinders are too small in proportion to the weight placed on the drivers, th.'n the engine cannot haul the train that it was intended it should do with the correct weight on the drivers. If, on the other hand, the cylinders are too large in proportion to the weight placed on the drivers, then the engine cannot employ all its tractive power. In these cases, there will be either a waste of material or steam. Here, then, we see that in a correctly designed engine there is a fixed relation or proportion between its tractive power and the weight placed upon the drivers. The tractive power is not only dependent upon the diameter of the cylinders, but also upon the diameters of the drivers, the length of stroke, and the mean effective steam pressure per square inch of piston. '2'2. In Fig. S we have represented a pair of cylinders and one of the front pair of driving wheels of an eight-wheeled engine, such as shown in Fig. 1. One of the cylin- ders in Fig. 8 is connected to the driving wheel; the other cylinder is connected to a crank fastened to the same axle, and not connected to a driving wheel, because we have assumed that there is only one driving wheel on the axle. Let us also assume that the cylinders in Fig. S, with frames, valve gear, and all necessary mechanism, are firmly fastened to blocks or a foundation, so that this figure represents a complete stationary engine. The driving wheel is not to touch the track, but the whole engine is set high enough so that a rope can be fastened to the lower part of the driving wheel, in such a manner that when the other end of the rope is attached to a train this rope will be parallel to the track, as shown. When this engine is set in motion in a direction as shown by the arrow, it will haul the train towards the engine. Now, the power that this engine exerts in doing this is precisely the same as the tractive power of a locomo- tive designed to do the same amount of work. Should the total weight of this train be 1,000 tons, then, according to what has been said before, it will take 7,500 pounds to move it, and therefore the stress or the pull on the rope will be 7,~>00 pounds. If, instead of fastening this rope to the train, we pass it over a pulley, , and attach a weight, tr, to it weighing 7,f>00 pounds, as shown by the dotted lines in Fig. 8, then the stress or the pull on the rope will not be changed, but will still remain as before, namely, 7, .">!)() pounds, and therefore we conclude that the power necessary to move the train is exactly the same as the power necessary to hoist a given weight. For the sake of clearness and simplicity, when calculating the tractive power of a locomotive, we shall hereafter always assume that the train resistance is represented by a weight, u; fastened by the means of a rope to ttc driving wheel, as shown in 12 MODERN LOCOMOTIVE COXSTRVCTION. Fig. 8, and that the cylinders must be made large enough so as to be capable of lifting this weight. But the reader may say that a locomotive has more work to do than the stationary engine here represented, because the locomotive must move its own weight, which the stationary engine does not have to do. This is true, but it must be remembered that we are allowing 7| pounds for every ton of the weight of train that is to be moved, and, as we have stated before, this may be considered and we do consider it so as not only sufficient to move the train, but also sufficient to move the weight of the locomotive and overcome the friction of its mechanism. Yet we must again call the attention of the reader to the fact, that any particular or given speed is not yet taken into con- sideration; we are simply proportioning an engine capable of moving a train vcry slowly. 23. The foregoing being thoroughly understood, the solution of the following example will not be difficult : EXAMPLE 4. Find the diameters of the cylinders for an eight-wheeled locomotive, whose total weight on drivers is 20,000 pounds, the diameter of the driving wheels, 45 inches ; the stroke, 20 inches ; and the mean effective steam pressure 90 pounds per square inch of piston area. (The writer believes that for the mean effective steam pressure 90 pounds per square inch is a good average, and this will always be adopted unless otherwise stated.) From what has been said before, we know that the total adhesive force will be -f of the weight placed on the drivers ; hence the total adhesive force will be of 20,000, which is equal to 4,000 pounds. We have also seen that the adhesion is equal to the train resistance; hence the weight ^v, in Fig. 8, which represents the train resistance, must weigh 4,000 pounds. Now, all we have to do is to find the diameters of the two cylinders, as shown in Fig. 8, capable of lifting this weight of 4,000 pounds; and so for all locomotives when the total weight on the drivers is known, no matter how many driving wheels are to be placed under an engine, we always assume that the train resistance is represented by the weight w; that all this weight, or train resistance, is applied to only one driving wheel; and that the two 13 cylinders must In- made largo enough, so that their combined effort mil be sufficient for lifting this one weight it; which \vc assume to be 4 of the total weight placed on all the drivers. In our example, as we have already seen, this weight w is equal to 4,000 pounds, and the diameters of the driving wheels 45 inches each. When the wheel has made one revolution, the weight tr will then have been raised through a distance equal to the circumference of the wheel, and this circumference is 141.37 inches, or 11.7S1 feet. lu raising this weight, a certain amount of energy must be expended; and, to know exactly how much has been expended, we must compare it to some standard or unit of energy. The amount of work required to raise or lift one pound one foot high is equal to a unit <>f energy or foot-pound; hence, if two pounds are lifted one foot high, two units of energy have been expended, or, if five pounds are lifted OIK* foot high, five units of energy have been expended; and, if the five pounds are raised five feet high, then 2."> units of energy have been expended, because, to raise the five pounds through the lirst foot, five units of energy will be required; to raise them through the second foot another five units will be required; the same for the third, and so on up to the fifth, making a total of 23 units of energy, or foot-pounds. In our example a weight of 4,000 pounds must be raised 11.781 feet high. To raise this weight through the first foot, 4,000 units of energy or foot-pounds will be required; and the same amount of energy will be required to raise it through the second foot, and again the same through the third foot, and so on until the height of 11.7S1 feet has been reached ; therefore, the total number of units of energy, or foot- pounds, that must be expended to raise this weight through a distance of 11.781 feet is 4,000 x 11.781 = 47,124 foot-pounds. In a similar w r ay, for all engines, we multiply the weight, it; in pounds, which represents the adhesion, by the circumference of the wheel in feet, and the product will be the number of foot-pounds or units of energy that must be expended during the time the wheel makes one revolution. Hut the energy necessary to raise this weight is derived from the steam pressure in the cylinder, and since the mean effective steam pressure prr square inch of piston is already given namely, !M) pounds it only remains to make the cylinder of such a diameter that we can obtain 47,124 units of energy for every turn of the wheel with a weight attached, as shown in Fig. 8. But now notice the fact that during the lime the wheel makes one turn, raising the weight 11.781 feet high, the piston travels 1 hrongli a distance equal to twice the length of the stroke; the stroke being 20 inches, the piston travels through a distance of 40 inches, or I!..'!,'; feet. During the time that the piston travels through a distance of :!.">:! feet, 47,124 units of energy or foot-pounds must be expended, and therefore, 47124 dividing 47,124 by .'!.)!:! feet, we have = 14,151 pounds. This last answer simply ).>> means that to raise the 4,000 pounds weight through a distance of 11.781 feet, the weight being attached to the wheel, as shown, will require as many units of energy as to raise a weight of 14,1.">1 pounds .'!.:!.'! feet high, the weight being attached directly to the end of the piston rod, as shown in Fig. 9. 14 MODEltX LOCOMOTIVE CONSTRUCTION. Now, it will be readily understood that the mean effective steam pressure on each square inch of piston will lift a portion of this weight of 14,lf>l pounds, and the amount that the pressure per square inch of piston will lift is 90 pounds; licncc, divid- ing 14,151 pounds by 90 pounds, we have = 157.2 square inches. This means t/\/ that the total piston area must be 157.2 square inches. But we have two cylindei's ; 157 2 therefore = 78.6 square inches in the area of one piston ; and a piston having an area of 78.6 square inches, must be 10 inches diameter. Hence a locomotive having four driving wheels, with 20,000 pounds placed upon them, the driving wheels being 4~> inches in diameter, and a mean effective steam pressure of 90 pounds per square inch, will require cylinders 10 inches in diameter and 20 inches stroke. Here we have calculated the diameters of the cylinders suitable for a given weight placed on the drivers. We may reverse the order of 1 his calculation, and find the necessary weight that must be placed on the drivers, when the dimen- sions of cylinders and diameters of driving wheels are given. EXAMPLE 5. The diameter of each cylinder is 10 inches; stroke, 20 inches ; diameter of driving wheels, 45 inches; mean effective steam pressure, 90 pounds per square inch of piston. What is the tractive power of such an engine ? And how much weight must be placed on the drivers I The area of a piston 10 inches in diameter is 78.54 square inches. Multiplying the area of the piston by the steam pressure per square inch, we have 78.54 x 90 = 7068.6 pounds total steam pressure on one piston ; but there are two pistons, hence 7068.6 x 2 = 14137.2 pounds, which is the total steam pressure on both pistons. The stroke is 20 inches, and during the time that the wheel makes one turn, the piston has traveled through twice the length of the stroke ; hence 20 x 2 = 40 inches, or 3.33 feet. Multiplying the total steam pressure on the pistons by 3.33 feet, we have 14137.2 x 3.33 = 47076.876 foot-pounds, or units of energy the cylinders can exert during one revolution of the wheel. The driving wheels are 45 inches in diameter ; hence the cir- cumference of each wheel will be 141.37 inches, or 11.78 feet. Dividing the units of energy the cylinders are capable of exerting by the circum- ference of the wheel, we have - - 3,996 * pounds. The tractive power of the 11.78 engine is, therefore, capable of lifting a weight of 3,996 pounds attached to the driving wheel, as shown in Fig. 8; or, in other words, the tractive power of this engine is capa- ble of overcoming a train resistance of 3,996 pounds. In a similar manner, the tractive power of any engine may be found, namely, by multiplying together twice the area in square inches of one piston, the mean effective steam pressure per square inch, and * Tliis answer would have been 4,000, instead of 3,996, if the decimal fraction iu the 3.33 feet (obtained by multiplying the stroke by 2) had been exact. rn\sri;n-no.\. 15 (win- tlit- length of tin- stroke in feet; then dividing this product by the circumference in feet of the wheel, the quotient will he the tractive power of the engine. This rule can be greatly simplified, as we shall presently show. The tractive! power and the adhesion are represented by the same number of pounds; therefore multiplying the tractive power by .">, we have :!,9!K> x :>=1!>,!)HO pounds, which is the weight that must be placed on the drivers of this particular engine. Ouv answer, then, to Kxample 5 is: Tractive power, 3,996 pounds; weight on drivers, 19,980 pounds. WEIGHT OF ENGINES. '24. In Kxample 4 it has been shown how to find the diameters of the cylinders when the weight on the drivers and the diameters of the same are known; and in Example ."> it has been shown how to find the weight on the drivers when the dimensions of the cylinders and diameters of driving wheels are known. From the reasoning connected with these examples, we conclude that the tractive power should not be more or less than the adhesion a fact which we have stated before. We may also reasonably con- clude that, when the dimensions of the cylinders and the diameters of the driving wheels of any engine are given, and if we assume that, in all cases, the mean effective steam pressure per square inch of piston is 90 pounds, we may at once arrange, for future use and reference, a table for each class of engine, showing the tractive power of each, the necessary weight on the drivers, and the number of tons of 2,000 pounds that each engine can haul on a straight and level track. Indeed, we may extend these tables so that the weight on the track, and consequently the total weight of each engine, will at once be seen. With these objects in view, the following tables have been prepared. In these tables, columns 1 and '2 are exactly the same as those given in tables 1, 2, 3 and 4. In column 3 of all the following tables the adhesion is given and, since the adhesion and tractive power are expressed by the same number of pounds, these figures are obtained by finding the tractive power of each engine, and for this purpose the small diameters of driving wheels given in column 2 are always used. The weight on drivers is shown in column 4, which is obtained by multiplying the adhesion by 5 for all classes of engines. Column 5 gives the weights on the trucks ; the calculations for these weights are based upon observations. Thus, it has been noticed that the weight on the truck for an eight-wheeled engine is about one-half of that placed on the drivers ; hence, multiplying the weight placed on drivers by the decimal ..">, the weight on the truck will be known. For Mogul engines, we multiply the total weight on drivers by the decimal .2, and the product will be the weight on the truck. For ten-wheeled engines, the total weight on the drivers multiplied by the decimal ..'!2 will be equal to the weight on the truck. And lastly, for consolidation engines, the total weight on drivers multiplied by the decimal .!<> will determine the weight on the truck. For instance, to find the weight on the truck for an eight-wheeled engine with cylinders 17"x 24", we multiply the total weight on drivers for this engine, given in column 4, by..">; hence, we have r>2,020 x.f> = 2(i,010 pounds, which is the weight on truck. 1(3 MODEM LOCOMOTIVE CONSTRUCTION. For a 17" x 24" Mogul engine, we have 63,697 x .12=1:2,7:!!) pounds = weight on truck. For an 18" x 24" ten- wheeled engine, we have 68,611 x .32 = 21,95.") pounds = weight on truck. And for a 20" x 24" consolidation engine, we have 90,000 x .16 = 14,400 pounds = weight on truck. In column 6, the total weight of each engine is given, which is obtained by adding the weight on the drivers to the weight on the truck. Dividing the adhesion given in column 3 by 7J, will give us the number of tons of 2,000 pounds that the engine is capable of hauling on a straight and level track; these figures arc given in column 7. The weight of engines given in these tables will be found to agree generally very closely with the actual weights of locomotives recently built, although it must not be expected that these weights will agree in every case with the actual weights, because different builders do not build their engines alike. The given weights on the trucks for Mogul or consolidation engines may differ considerably from the actual weights, yet this should not be a matter of surprise, because the weight on a truck for either of these engines can be changed without changing the total weight of engine, and, indeed, often the pieces of mechanism con- necting the truck to the engines are so arranged that a heavy or light weight can be thrown on the truck while the engine is standing on the track. Yet the figures in these tables, indicating the weights on the trucks, can be safely taken as guides in constructing and proportioning an engine. The actual weight on trucks for eight-wheeled or ten-wheeled engines will not differ much from those given in the tables, because these weights depend greatly on the difference between the total and rigid wheel bases, and these are not often changed by the different builders. The ratio of the rigid and total wheel buses is generally the same in all eight-wheeled engines, and the same may be said of ten-wheeled engines. It has already been stated that the rule (as before given) for finding the tractive power of an engine can be greatly simplified. To explain this, we will again state the former rule, but, instead of writing it in the ordinary language, we will employ a num- ber of simple arithmetical signs. This will enable us to bring the whole mode of operation under the eye, and follow it without taxing our memory ; hence this rule will read as the following : EULE A. Area of piston in so. in. x mean effective steam pressure per sc[. in. x stroke in ft. x L' 2 = tractive power. Circumference of driving wheel in feet For the sake of distinction we have called this Rule A. Now, remembering that the area of a piston is found by multiplying the square of its diameter by .7854, and also that the circumference of a wheel is found by multiplying its diameter by 3.1416, we can put in the place of "area of]>i*tii hi xi/ittin 1 inches," in Rule A, the method of finding this area, namely, square of diameter in inches x .7854; and, in the place of "cireinnji'rciifc of irlu'rl in fret," we may put diameter of wheel in feet x 3.1416; conse- quently, the wording of the Rule A will be changed, and read like Rule B : < <>\sri;r<'n<>\. 17 RULE B. Sq. of diam. of piston in in. x .7854 x mean effective steam pressure |>er sq. in. x stroke in ft. x 2 x 2 Diameter of driving wheel in feet x 3.141(1 = tractive power. If, now, we multiply the decimal .7854 by 2, and again by 2 (figures which are found above the line in Rule B), we have a product of 3.1416. Below the line, in Rule B, we find the same figure that is, 3.1416 ; hence we may cancel all these figures, or, in other words, we may throw out of the Rule B the decimal .7854 and the figures 2x2, all found above the line, and the figure 3.1416, which is found below the line. Doing so, the wording of the Rule B will be changed to that of = tractive power. RULE 3. Square of diameter of one piston x mean effective steam pressure per square inch x stroke in feet Diameter of driving wheel in feet Iii ordinary language, Rule 3 would read: multiply together the square of the diameter in inches of one piston, the mean effective steam pressure per square inch and the length in feet of one stroke. The product thus obtained, divided by the diameter in feet of one wheel, will be the tractive power. EXAMPLE 6. What is the tractive power of a locomotive whoso cylinders are 17 inches in diameter and 24 inches stroke? The mean effective steam pressure is 90 pounds per square inch, and the driving wheels 60 inches in diameter. 17 x 17 x 90 x 2 = 10404 = tractive power. If the tractive power had been calculated according to Rule A, the result would have been the same. But Rule 3 is evidently the simplest, and a great amount of time and labor will be saved by using it. All the figures expressing the adhesion in pounds, as shown in column 3 in all the following tables, have been found according to Rule 3 : TABLE 5. EIGHT-WHEELED LOCOMOTIVES. Cylinder*. Diameter. Stroke. Diameter of Driving Wheels. AtllicM'.n. Weight on Drivers. Weight on Truck. Total Weight. Hauling Capacityon Level Track In Tons of 2,000 Pounds, in- cluding Tender. Column 1. Column 2. Column 3. Column 4. Column 5. Column <;. Column 7. Inch 1 -. Inches. Lbe. Lbe. Lb*. Los. in 2H 4.1 to 51 4000 90000 101 II III 80000 533 U x 22 45 to 51 5324 26620 18810 39930 709 ]_' 22 48 to 54 5940 2!>700 1 1 *.-,(! 44550 792 13 x 22 49 to 57 6828 3414(1 17(171) 51210 BIO 14 x 24 f>. r . to 61 Tti'.iT 384K.-) L9242 57727 1026 15 , 21 .V> to lili 8836 441 HO 221 I'll) <>(i270 1 17s 16 x 24 r.s to 66 BBSS 4706;-) 23832 71497 1271 17 x 24 60 to 66 1(14114 S30X M01Q 78080 1887 18 x 24 6i to 'it; 11472 57380 28680 86040 1529 in columns 1 and 2 an- tin- s:iine ;is those in Table 1. Figures in column 3 arc ol>taiue<l acrordiiix to Kule 3. 18 M<H>EI;\ Figures in column 4 are obtained by multiplying the figures in column :j by 5. Figures in column 5 are obtained by multiplying the figures in column 4 by .5. Figures in column 6 are obtained by adding the figures in column 4 to those in column 5, and are the weight of engines in working order with water and fuel. Figures in column 7 are obtained by dividing the figures in column 3 by 7. TABLE (>. MOGUL ENGINES. Cylinders. Diameler. Stroke. Diameter of Driving Wheels. Adhesion. Weight on Drivers. Weight on Trucks. Total Weight. Hauling Capacity on Level Track in Tom of 2,COO Pound*, in- cluding Tender. Column 1. Column 2. Column 3. Column -1. Column 5. Column 6. Column 1. Inches. Inches. Lbs. Lbs. Lbs. Lbs. 11 x 16 35 to 40 4978.2 24891 4978 29869 663 12 x 18 36 to 41 6480 ;ii'40o 6480 38880 864 13 x 18 37 to 42 7399.4 36997 7399 44396 986 14 x 20 39 to 43 9046 45230 9046 54276 1206 15 x 22 42 to 47 10607 53035 1(101)7 63642 1414 16 x 24 45 to f>l 12288 61440 1 22SS 73728 1638 17 x 24 49 to 54 12739.5 63697 1 2739 76436 1698 18 x 24 51 to 56 13722.3 68611 13722 &i:u:\ 1828 19 x 24 54 to 60 14440 72200 14440 86640 1925 Figures in columns 1 and 2 are the same as those in Table 2. Figures in column 3 are obtained according to Rule 3. Figures in column 4 are obtained by multiplying the figures in column 3 by 5. Figures in column 5 are obtained by multiplying the figures in column 4 by .2. Figures in column 6 are obtained by adding the figures in column 4 to those in column 5, and are the weight of engines in working order with water and fuel. Figures in column 7 are obtained by dividing the figures in column 3 by 7. TABLE 7. TEN-WHEELED ENGINES. Cylinders. Diameter. Stroke. Diameter of Driving Wheels. Adhesion. Weight on Drivers. Weight on Truck. Total Weight, with Water and Fuel. HanlingCapacitvon Level Track in Tons of 2,000 Pounds, in- cluding Tender. Column 1. Column 2. Column 3. Column 4. Column 5. Column 6. Column 7. Inches. Inches. Lbs. Lbs. Lbs. Lbs. 12 x 18 39 to 43 5981.5 29907 9570 39477 797 13 x 18 41 to 45 6677.5 33387 10683 44070 890 14 x 20 43 to 47 8204.6 41023 13127 54150 1093 15 x 22 45 to 50 9900 49500 15840 65340 1320 16 x 24 48 to 54 11520 57600 18432 71:0:12 1536 17 x 24 51 to 56 12240 61200 1 9584 80784 1632 18 x 24 51 to 56 13722.3 68611 21955 90568 1829 19 x 24 54 to 60 14440 721200 23104 95304 1925 Figures in columns 1 and 2 are the same as those in Table 3. Figures in column 3 are obtained according to Rule 3. Figures in column 4 are obtained by multiplying the figures in column 3 by 5. Figures in column 5 are obtained by multiplying the figures in column 4 by .32. Figures in column 6 are obtained by adding the figures in column 4 to those in column 5, and are the weight of engines in working order with water and fuel. Figures in column 7 are obtained by dividing the figures in column 3 by 7A. MI>IU:I;\ i.nm MI >n 1 i-: t <>\sn;i CTIOX. 11) TABLE 8. CONSOLIDATED ENGINES. rvlinilere. Diani.-u-r. Stroke. Dianu-U'r of Driving WhoclB. Aillii-iiin. Weight on Drivers. Weight on Truck. Total Weight, with Waivr :ind Fuel. Haulm); Capacity on Level Track in Tons of iOIX) Pounds, in- cluding Tender. Column 1. Column S. Column 3. Column 4. Column 5. Column 6. Column 7. Inches. Inches. Lbe. UN. Lb. LOB. 14 x 16 i:> x 18 Jn x 24 21' - I'l :;r. to 38 36 to 38 4S to 50 .in to 52 7840 10128 18000 20908.8 88200 5061;.-) !M)000 104544 6272 8100 14400 16727 45472 58725 104400 121271 1045 1390 24(10 2787 Figures in columns 1 and 2 are the same as those in Table 4. Figures in column 3 are obtained according to Rule 3. Figures in column 4 arc obtained by multiplying the figures in column 3 by 5. Figures iu column 5 are obtained by multiplying the figures in column 4 ly .16. Figures in column 6 are obtained by adding the figures in column 4 to those in column 5, and are the weight of engines in working order with water and fuel. Figures in column 7 are obtained by dividing the figures in column 3 by 7|. CHAPTER II. CONSTRUCTION OF CYLINDERS. STEAM PIPES. SLIDE-VALVES. 25. The general practice in the United States is to place the cylinders outside the frames A, A, as shown in Figs. 10 and 11 ; but on further examination of these two figures, we find that there is a considerable difference in the construction of the cylin- ders, so that we may divide these into two classes. In one class we may place the cylinder with half the saddle cast in one piece ; and in the other class we may place the cylinder with the saddle cast separate. The following explanation will help the reader to gain a clearer understanding of the difference of these constructions. Fig. 10 shows an end view of a cylinder with half the saddle cast to it. In this case the cylinder casting is extended over the frame A to the center of the boiler, and here meets a similar extension from the opposite cylinder (not shown in this figure), the two being bolted together by the bolts I, b, b. These extensions of the cylinders, or those parts of the castings which extend from frame to frame, constitute the cylin- der saddle ; hence this type of cylinder is known by the term " cylinder and half-saddle cast in one." 26. Fig. 11 shows a locomotive cylinder belonging to the second class, in which the saddles are cast separate, the cylinder being bolted to the saddle by the bolts C, C; the manner of fastening these to the frames is similar to that of the former cylinders. Cylinders with half-saddle cast in one are generally used, because only one pattern is needed for both cylinders in a locomotive ; whereas, the saddle being cast separately, we need a greater number of patterns. 27. In this chapter we will consider only the cylinders with half-saddle cast in one because they are the most popular ones. The arrangement of the steam-ways, steam passages, exhaust passages, as well as all other details of these cylinders, are shown in Figs. 12, 13, and 14. Fig. 12 shows a section lengthways of the cylinder, the section being taken through the line a, b, drawn in Fig. 14. Fig. 13, right-hand side, shows a section of the cylinder and saddle taken through a line c, rf, drawn in Fig. 14. Fig. 13, left-hand side, shows an outside end view of the cylinder and half-saddle. Fig. 14 shows a plan of the cylinders and saddle ; the right-hand side of this figure shows a section of half the saddle, the section being taken through the line c, f, drawn in Fig. 13. Similar letters in these three views indicate the same pieces or parts of the cylinder and saddle. In Fig. 12 the cylinder heads, piston, and piston-rods are shown, but these h.-ivc been omitted in all the other figures. \min-:i; v i.<H-.Mnri\'E ro\sTi;rrrin\. 21 .1, .1 are sections of the frames to which the cylinders are firmly bolted. /.' represents the cylinder. (' represents the back cylinder head. 1) represents the front cylinder head. E represents the piston. /'represents the piston-rod. (i represents the piston-rod gland. // represents steam-chest seat, that is, the surface on which the steam-chest rests I represents the valve seat, that is, the surface on which the slide-valve moves backward and forward. J represents the steam passage. This steam passage terminates at 01 nd (that is, the end in the saddle), with a round hole, as shown at J\. Before this passage reaches the other end, it is divided into two brandies, each one terminating in the 22 MODJSRN LOCOMOTIVE CONSTRUCTION. steam-chest seat with the openings marked ./ 2 , J.% an( l both of these openings lie inside the steam-chest (the steam-chest is not shown in these illustrations). 28. By dividing this steam passage into two branches three advantages are gained. First, the steam will be delivered at each end of the steam-chest, so that the steam can freely enter the steam ports. Second, a right and left-hand cylinder pattern will be avoided, and only one pattern needed for both cylinders. Third, if the cylinders are accurately planed and fitted to gauges, they will be interchangeable ; that is, we can use such a cylinder for either side of the engine. 29. The duty of the steam passage is to conduct the steam into the steam-chest ; the steam enters the opening J lt and is delivered into the steam-chest through the open- ings J 2 , J 2 . This is the only duty the steam passages have to perform, and consequently the steam in these passages will always flow in one direction, as shown by arrows 2. 30. K represents the exhaust passage. This terminates with one opening in the valve seat, and this opening, marked K lt is called the exhaust port ; the other end ter- minates with a round opening K 2 , a little above the saddle. Some designers make the form of this opening a semicircle ; others, again, will make it a square or oblong ; and which of these forms is to be adopted will depend greatly upon the judgment and fancy of the designer. The duty of the exhaust passage is to conduct the steam out of the cylinder after it has performed its work. In this passage the steam will always flow in a direction as indicated by arrow 3. 31. On each side of the exhaust passage, Fig. 12, is a channel or passage marked L L ; these passages are called the steam- ways. For the sake of distinction we shall call the steam way nearest the front cylinder head, the " front steam- way," and the other one, the " back steam- way." These steam- ways terminate with the openings L^ L l in the valve seat, and these openings are called the steam ports. The steam-ways have a double duty to perform, namely, they must conduct the steam into the cylinder, and after the steam has performed its work, they must conduct the steam out of the cylinder. For instance, when the piston stands in the position as shown in Fig. 12, the steam will be conducted through the front steam-way into the cylinder space between the front cylinder head and piston, and the steam will flow through this steam- way in a direction as shown by arrows 4. On the other side of the piston the steam is conducted out of the cylinder, flowing through the back steam-way in a direction as indicated by arrows 5. But now, when the piston stands near the back cylinder head, then the back steam - way will conduct the steam into the cylinder, the steam flowing in an opposite direction, to that shown by the arrows 5, and, in the meantime, the front steam-~\v;iv will conduct the steam out of the cylinder, causing it to flow in an opposite direction to that indicated by the arrows 4. Here, then, the reader will perceive what was meant by saying the steam-ways have a double duty to perform. We draw particular attention to this fact, as we shall allude to it again. The metal or small bars marked M, between the steam ports and the exhaust port, are called bridges. 32. N, N represent the cylinder cocks. represents the boiler, or to be more precise, the smoke-box of the boiler, to which the cylinders are firmly bolted as shown. ro.\sri:r<-ri<>\. 23 PISTON AND ENGINE CLEARANCE. 33. Piston clearance is the distance /' between the piston and cylinder head at the end of a stroke. In locomotive cylinders it varies from to inch; it is generally equal to I of an inch. The term " piston clearance" must not be confounded with the term "engine clearance," or simply clearance, which is the space between the piston and head plus the volume of the steam-way, or we may say, that the engine clearance is the whole minimum space between the piston and the valve face at the completion or beginning of a stroke. COUNTERBORE. 34. The cylinder is counter-bored at each end, generally J of an inch larger in diameter than the bore of the cylinder. The depth of the couuterbore should be such, that when the piston stands at the end of a stroke, as shown in Fig. 1'2, the packing ring, //, will not project more than $ of an inch beyond the edge of the couuterbore, or when the piston stands at the opposite end of the stroke, the packing ring, /(, will not project more than i of an inch beyond the edge of the corresponding counterbore. In any case care must be taken to regulate the depth of the couuterbore so as not to allow the whole width of any of the packing rings to pass over it. It will be readily under- stood that should any of the packing rings travel beyond the edge of the couuterbore, they will at once adjust themselves to the larger diameter, and thus prevent the piston from returning without doing considerable damage. :!.">. For the cylinders such east-iron should bo selected as will wear well and equally; it must be hard and homogeneous, yet not so hard as to prevent the tools from cutting during the process of boring, planing, drilling, and turning. .'!;. The joints beween cylinder and cylinder heads are made metal to metal, and ground; the part to be ground is allowed to project a little beyond the face of the flange, as shown in Figs. 12 and 14. The bolts securing the cylinder heads to the cylinder are usually placed from 4 to :>A inches from center to center, and these distances will determine the number of bolts to be used. Their diameter should be such that the stress brought upon them by the steam pressure alone will not exceed 5,000 pounds per square inch. CYLINDER PROPORTIONS AND DETAILS. 37. To find the diameter of a cylinder-head bolt we must first know the initial steam pressure in the cylinder, that is, the steam pressure at the beginning or near the beginning of the stroke. We believe that 12u pounds per square inch for the initial steam pressure \\-jH agree very closely with ordinary practice, but the tendency is to work with higher steam pressure than this. Assuming that 1'JO pounds per square inch for the initial pressure is correct, the diameters of the bolts for the cylinder head can easily be found. For example, let it be required to find the diameter of tl ylinder-head bolts, the cylinder being l<i inches in diameter, and the bolts to be placed about ~> inches from center to center. 24 MODERN LOCOMOTIVE CONSTRUCTION. The area of a circle 16 inches in diameter is 201 square inches; multiplying this area by the initial steam pressure per square inch, we have 201 x 120 = 24,120 pounds ; this is the force which the combined strength of all the bolts in one cylinder head must be capable of resisting, independent of the stress that is already placed on these bolts by the use of the screw wrench. Placing these bolts about 5 inches from cen- ter to center, we find that twelve bolts are needed. Dividing the 24,120 pounds by 12, we have ^^- = 2,010 pounds. This means that each bolt must be capable of resisting a pulling force of 2,010 pounds. Tlio area of the cross-section of a bolt must be such that each square inch will be subjected to a stress of not more than 5,000 pounds. But now the pulling force on the bolt is less than 5,000 pounds, hence the area will also be proportionately less than one square inch. Therefore, to find the area of cross-section of the bolt we divide 2,010 by 5,000, and ffcro = -4 5 this means that the area of the cross-section of the bolt must be TO of a square inch, and consequently will be very nearly $ of an inch diameter. Adding to this diameter, twice the depth of thread, we find that the bolts for a 16-inch cylinder head should be & of an inch in diameter. 38. Some master mechanics object to bolts in the cylinder head, and demand studs in place of them. Their objection to bolts is, that in case a bolt should break, the whole cylinder lagging (marked _R, R in Figs. 12 and 13) must be taken off in order to place a new bolt in position. On the other hand, should a stud break, that part left in the cylinder flange can be drilled out, without disturbing the cylinder lagging, and hence the preference for studs. 39. The cylinder lagging consists of strips of ordi- nary pine fitted around the cylinder, the thickness of these strips filling the whole space between the body of the cylinder and the outside of the flanges. The writer believes that a few thicknesses of asbestos paper placed around the cylinder, and then the remaining space filled with wood, as shown in Figs. 12 and 13, is the best practice. 40. Figs. 15, 16, 17, 18, and 19 show the thicknesses of metal in locomotive cylinder heads, cylinders, and their flanges. These dimensions have been obtained by actual measurements of the metal in cylinders belonging to acknowledged first-class modern locomotives, and suitable for an initial pressure of 120 pounds per square inch. In these figures it Moi>Ki;\ /.(icoMorirK coxsrari'Tiox. 25 will be noticed that the cylinder flanges are considerably thicker than those of the cylinder head; this is certainly a good practice, because in case a fracture should take place through some obstruction between cylinder head and piston, the break will occur in the cylinder head, and not in the cylinder flange; and thus, on account of the comparative cheapness with which a cylinder head can be replaced, costly repairs and vexing delays wih 1 be avoided, such as are sure to follow when the cylin- der flange is injured. 41. In order to insure a good cylinder casting, the thickness of the bridges should be about the same as that of the cylinder barrel, and the thickness of metal around the exhaust passages, the steam passages, and sides of the saddle may be made about ^, of an Inch less for the smaller cylinders, and about of an inch less for the larger cylin- ders. 4 It sometimes occurs in connection with railroads, that ferry-boats must be used in which the cylinders are very large in diameter. To determine the thickness of metal in these cylinders, the following facts must betaken into consideration : first, the thickness of metal must be such, that when the cylinder is subjected to the maximum steam pressure, fracture cannot take place ; second, a sufficient amount of metal must be allowed for reboriug ; third, the cylinder must be sufficiently stiff to prevent jarring during the process of boring and planing ; and lastly, cylinders must be sufficiently strong to maintain their circular form. Rules for finding the thickness of metal in cylinders that will satisfy all the foregoing demands have been given by a number of eminent writers. The following rule has been copied from J. D. VanBuren's book on " formulas for the strength of the iron parts of steam machinery." In the writer's opinion this is the best rule, and will always give the proper thickness for all marine or stationary steam- engine cylinders. For locomotive cylinders the thickness found according to this rule will be rather light when compared with the thicknesses given in Figs. 15, 16, 17, 18, and 19. EULE 4. To find the thickness of metal in cylinders : Multiply the diameter of the cylinder in inches by the steam pressure per square inch, also multiply this prod- uct by the constant decimal fraction .0001; add to this last product the square root of the diameter of the cylinder in inches multiplied by the constant decimal fraction .15; the result will be the thickness of metal in the barrel of the cylinder. Or we may write this rule thus : (Diam. of cyl. in inches x steam pressure persq. inch x .0001) + .15 ^/diam. of cyl. in inches = thickness of cyl. wall. EXAMPLE 7. What must be the thickness of metal in the barrel of cylinder, 49 inches in diameter, for (ill pounds' steam pressure per square inch! (4!) x (JO x .0001) + .15 V49~= 1.34 inch = thickness of metal. Now let us find, according to rule, the thickness of metal in a locomotive cylinder 16 inches diameter. Assuming that the greatest steam pressure these cylinders have to resist is 1'JO pounds per square inch, we have (16 x 120 x .0001) + .15 v/Ui = .7920 of an inch, 26 MODERN LOCOMOTIVE CONSTRUCTION. that is, the thickness of metal in the barrel of cylinder should be fully ;| of an inch. Comparing this thickness with that given in Fig. 16, we find that the thickness found according to this rule is light; in locomotive cylinders it should have been oue.inch, ;is shown. By a little reflection we can discover the reason why the thickness of metal in locomotive cylinders should be more than in cylinders for marine or stationary engines. In locomotive cylinders more metal must be allowed for reboring than in cylinders for the other classes of engines, because in a locomotive the piston speed is generally very high, and besides this, in locomotive engines ashes accumulate around the exhaust nozzle iu the smoke-box, and should then the engine be in motion with steam shut off (which occasionally occurs), ashes are sometimes drawn in the cylinder through the exhaust passage, and the consequence of such an evil, and the necessity of reboring, can easily be conjectured. Hence, the thickness of metal in a cylinder found according to this rule should be increased from to J of an inch for locomotives. STEAM PORTS AND EXHAUST POET. 43. Figs. 20 and 21 show the steam ports and the exhaust port. The form of these, also the length, breadth, and area of the same, are now to be considered and deter- mined. In Fig. 21 it will be noticed that the ends of the steam ports have the form of a semi-circumference of a circle, and the straight lines surrounding the exhaust port are joined by arcs, whose radii are equal to those of the semi-circumferences of the ends of the steam ports. Ports formed in this manner are superior to ports with square ends, because the sliding surface of the valve, and the valve seat having square- Fiff.20 ended ports, are liable to wear into grooves and ridges, particularly at the angles. Again, making the ends of the ports semicircular, as shown, adds strength to the bridges. This form of ports will also enable us to true up the whole port with a milling tool, and facilitate the application of a template which is to guide the milling tool, thus pro- viding for making the ports in all cylinders of one class exactly alike in regard to length, breadth, and distance between them ; such accuracy is a matter of great importance in locomotive engineering. The length of a steam port is, within certain limits, a matter of choice. The length is often made eqiial to the diameter of the cylinder, sometimes a little less, but should never be less than ? of the diameter of the cylinder. When the length of a steam port LOCOMOTIVE CONSTRUCTION. 27 has been established, then its breadth must be such that the port will have the proper area. Here, tlit'ii, we see that before both the length and the breadth of a port can bo decided upon, tin- area of the port must he known. We have already pointed out in Art. 31 that the steam-way lias a double duty to perform, namely, to admit steam into the cylinder, and to conduct it out of the same. To conduct the steam out of the cylinder requires a steam-way of greater cross-section than that which simply admits the steam; and since the port area really represents the cross-section of a steam-way, we conclude that the port area for conducting the steam out of the cylinder must be greater thau would lie required for admitting the steam. The reason of this is that, when the steam is admitted into the cylinder, the pressure of the steam is very nearly constant, because the pressure is sustained by the How of steam from the boiler, and, consequently, the velocity of the steam will be nearly constant. But, on the other hand, when the steam is allowed to escape, the pressure of the steam is generally less than it was when it entered the cylinder, and therefore the velocity of the steam will be slower. Again, as the steam continues to escape the pressure in the cylinder becomes gradually lower, and consequently the velocity also decreases. Now, the steam must be discharged as quickly, or nearly so, as it was admitted; but, since the velocity of the steam is slower when it (lows into the air than when it flowed into the cylinder, the area of the steam port for the release of steam must be larger than the area that would be required for the admission of steam. Wo therefore conclude that if the area of a steam port is largo enough for the release of steam, it will always bo large enough for the admission of steam. We find in the valuable work of D. K. Clark on "Railway Machinery," that for a piston speed of 000 feet per minute, a good exhaust will be obtained when the area of the steam port is ,' the area of the piston, the steam being in an ordinary state as to dryness. Assuming that for a slower piston speed the area of the steam port must be proportionately less, and for a faster piston speed proportionately larger, we have all the data necessary to find the area of the steam port suitable for any given diameter of cylinder and piston speed. Now, since for a piston speed of GOO feet per minute the port area must be -fa of the area of the piston, and for other speeds the port area must be in proportion, we may put our data in the following form: 600 is to the given piston speed in feet as -^ of the piston area in inches is to the port area ; or thus : li(M) : the given piston sp 1 in feet : : ny of the piston area in inches : the port area. But writing our data in this form, we recognize a statement of the simple rule of proportion ; in order, then, to find the required port area, we must follow the rule of proportion, consequently we have Rule 5. (liven piston speed in feet per minute x .1 ( . ( M , = port area in fractional parts of piston area. In ordinary language this rule would read: The given piston speed in feet per minute multiplied by ,',,, and this product divided by GOO, will be equal to the port area in fractional parts of the piston area. 28 MODERN LOCOMOTIVE CONSTRUCTION. Then, multiplying the area in square inches of the piston by the port area found by Eule 5, we obtain the number of square inches that the steam port area must contain. EXAMPLE 8. Find the steam port area suitable for a cylinder 17 inches in diameter, and a piston speed of 650 feet per minute. According to Rule 5, we have 650^1 600 that is, the port area must be equal to . part of the piston area. The area of a piston 17 inches in diameter is 226.98 square inches, hence 226.98 x .108 = 24.51384. This means that the steam port area must be equal to 24 square inches for this partic- ular piston speed. Of course, for a slower piston speed, this port area should be less. For instance, if the piston speed is to be 500 feet per minute, and the diameter of the cylinder 17 inches, as before, we have 500 x .1 ~~600~~ ' 3; and the piston area 226.98 x .083 = 18.8 square inches for port area. With the aid of Rule 5 we may arrange the following table, showing the ratio of port area to piston area. This table will be found usefiil and convenient, because with it the area of the steam port can be found with less time and labor. TABLE 9. PROPORTIONAL STEAM PORT AREA. Speed of Piston in Feet Per Minute. Port Area in Fractional PartB of Piston Area. 200 033 250 041 300 050 350 058 400 . . .066 450 075 500 083 550 . . .091 600 1 650 108 700 116 RULE 6. To find, with the aid of Table 9, the area of a steam port suitable for a given diameter of cylinder and a given piston speed : Multiply the area in square inches of the piston by the decimal fraction found in Table 9 on the same line that the given piston speed is indicated, the product will be the steam port area in square inches. EXAMPLE 9. Find the area of a steam port suitable for a cylinder 14 inches in diameter, and a piston speed of 450 feet per minute. The area of a piston 14 inches in diameter is 153.9 square inches ; referring to the piston speed of 450 feet in the Table 9, we find on the same line the decimal fraction .075, hence 153.9 x .075 = 11.5425 ; that is, the steam port area should be equal to ll square inches. We have already stated that the length of the steam port should be equal, or very nearly so, to the diameter of the cylinder, and not less than of the same. If, then, 'i-: c()\xTi;r<-Ti<>.\ the length has been decided upon, we simply divide the area of the steam port by the length, and tin- quotient will be the necessary width of port. Or, if we are compelled to adopt a certain width for the steam port, we divide the area of the port by the width, and the quotient will be the length of the port. In these calculations, for the sake of simplicity, we consider the ports to have square ends, as the area that is lost in making the ends circular is so small that it may be neglected. 44. The length of the exhaust port is always made equal to that of the steam port. For finding the breadth of the exhaust port, a graphic process has been here adopted, and such as, the writer believes, will be easy to follow and understand. Fig. "22 shows a section of a slide-valve, exhaust and steam ports. The valve is shown to stand in two positions on the valve seat. When in the position marked A the valve stands in a central position, that is, midway of its extreme travel, and when in position U it l< Lcnytlt-of-l-alve-seat Fig.22 stands at one end of its extreme travel. In this latter position we notice that the opening of the exhaust port is considerably contracted, and should, then, the opening C be much smaller than the width of the steam port, the free escape of the exhaust steam would be interfered with. We consider it to be good practice to make the exhaust port wide enough so that when the valve stands in an extreme position, as at B, the opening C will then be equal to the width of the steam port. Therefore, to find the width of the exhaust port, first indicate on paper the width of the steam port and the thickness of the bridge (see Fig. 23). On these draw a portion of the slide valve in an extreme position, as shown, and then make the exhaust port wide enough so that the opening C' will be equal to the width of the steam port. Generally, when this rule is followed, the width of the exhaust port will be equal to about twice that of the steam port for locomotive engines ; hence it is often said, that the width of the exhaust port should be equal to twice that of the steam port for all engines. This statement should be received with caution, as it might lead to error. Following the graphic method here explained, satisfactory results will always be obtained. l~i. The valve seat for locomotive cylinders is generally raised one inch above the surrounding surface, so as to allow for wear. 30 MODEKX LOCOMOTIVE CONSTRUCTION. The length of the valve seat (see Fig. 22) should be such that the valve may con- siderably overshoot it at each end of the travel when in full gear ; this will promote uniformity in wear, but care must be taken not to make the valve seat too short, because then the steam would pass underneath the valve into the steam port. STEAM PIPES. STEAM AND EXHAUST PASSAGES. 46. Figs. 24 and 25 show the steam pipes and the manner of connecting these to the cylinders. The steam pipe has only one duty to perform, namely, conducting the Section of Steam-pipe ii'jli lite line tj /,- Fig 24 OD o o o o o o o o Fig.25 steam to the cylinder, and therefore its cross-sectional area is made less than the area of a steam port through which the steam is both admitted and exhausted. It has been foimd that for a piston speed of 600 feet per minute good results will be obtained when the cross-section area of the steam pipe is equal to .08 (that is, y^) of the area of the piston ; for slower piston speeds proportionally less, and for higher piston speeds proportionally greater. Consequently, to find the cross-sectional area of a steam pipe, we again apply the rule of proportion, thus : 600 : given piston speed : : 0.08 : steam-pipe area in fractional parts of piston area. From the foregoing remarks, we can establish RULE 7. Multiply the given piston speed in feet per minute by the decimal .08, and divide the product by 600; the quotient will be the cross-sectional area of the steam pipe in fractional parts of the piston area. Or, writing this rule in the form of a formula, we have Given piston ^dper minute x .08 = steam . pipe area in fractiona i parts o f piston area. Then, multiplying this proportional area by the piston area in square inches, we obtain the number of square inches in the steam-pipe area. Mni>i-:it\ r.v.s-/7,vry/r>.v. 31 K \AMPLE 10. Find tin; cross-sectional steam-pipe area suitable for a cylinder 17 inches in diameter, and a piston speed of 500 feet per minuto. According to Rule 7, wo have 500 x .08 (iOO = .0666 This moans that the steam pipe area must bo equivalent to r^rfj, of the piston area. The area of a piston 17 inches in diameter is 220.98 square inches; there- fore, 22ti.98 x .Ou'b'G = 15.11b'8G8. That is, the cross-sectional steam-pipe area should be 154 square inches. With the aid of Kule 7, the following table has been arranged, showing the ratio between the steam-pipe area and the piston area for different speeds. I'sing this table when the steam-pipe area is to be found, time and labor will be saved. To find the cross-sectional area of the steam pipe with the aid of this table, we have 1 b'ri.K 8. Multiply the area of the piston in square inches by the decimal fraction found in Table 10, on the same line that the given piston speed is indicated ; the prod- uct will be the number of square inches in the cross-sectional area of the steam pipe. TABLE 10. PUOPOUTIONAL, STEAM-PIPE AllEA. Speed of Piwton in Feet Per Minnie. st<-:iin-jiijir Area in Fractional Parti" c>f Piston Area. 200 0"6 250 033 300 04 350 046 400 053 450 06 500 066 550 073 600 '. . . . 08 (l.'iii 086 700 093 EXAMPLE 11. Find the steam-pipe area suitable for a cylinder 16 inches in diam- eter, and a piston speed of 451) feet per minute. Referring to Table 10, we lind on the same line with the given piston speed of 450 feet the decimal .0<i. The area of a piston l(i inches in diameter is I'd] square inches; therefore, i>()l x .06 = 12.06. That is, the steam-pipe area should contain 12 square inches. 47. In Fig. 24, the area of the opening / of the steam passage should be the same as that of the steam pipe, because the steam passage is a continuation of the steam pipe. Consequently, when we know the area of the steam pipe, we also know the area of the opening./, and when we know the area of this opening, its diameter is easily found by referring to a table of areas of cin-Ies, or by one of the simple rules of men- suration. From these remarks, we may convetly infer that, for instance, a cylinder 17 32 MODERN LOCO MOTIVE CONSTRUCTION. inches in diameter and a piston speed of GOO feet per minute will require a larger ami in the opening J than the same cylinder would require for a piston speed of 500 feet per minute ; and, since the piston speed is not the same in all locomotives, we would naturally expect to find a number of core boxes of different size for each cylinder, so that the size of a steam passage could be changed in a cylinder pattern to suit some particular piston speed. To carry out such a system would require too great a variety of patterns ; and to avoid this, master mechanics and manufacturers generally group the cylinders, according to their diameter, into different classes, and adopt for each class some particular diameter for the opening J. In the following table, in column 2 are given the diameters of the openings J for the different classes of cylinders, such as are generally adopted ; of course, some makers will vary slightly from these figures. In column 3 the diameters of the exhaust open- ing (marked K, Fig. 24) are given. If these exhaust openings are made square, or of some other form, their area should contain about the same number of square inches as the circular openings corresponding to the diameters given in column 3, Table 11. TABLE 11. SIZE OF STEAM AND EXHAUST OPENINGS. Column I. Column 2. Column 3. Diameter of Cylinders. Diameter of Steam Opening /, in Inches. Diameter of Exhaust Opening K. in Inches. 10 3 34 11 3 3i 12 3i 4 13 3i 4 14 4i 5 15 4i 5 16 4 5 17 4} 5 18 4i 5 19 4f 5 20 5 5 22 5 5 i When an engine is to be designed for a very fast speed, we would advise to deter- mine the area of the opening J according to Rule 7, and not follow the diameters given in the last table. The area of any cross section of the steam passage should contain the same number of square inches as the opening J. In regard to the exhaust passage, good results will be obtained when the area of any cross section in the neighborhood of the line a I, Fig. 24, is made larger than the exhaust opening K; in fact, we have always obtained good results by making it as large as possible. With large exhaust passages the flow of exhaust steam will not be so irregu- lar as when smaller passages are used. In the writer's opinion, large exhaust passages will improve the draft of an engine, and to some extent lessen the back pressure in the cylinder. No rules have been established to determine the area of the exhaust 33 opening K- The (liaint'ter for these openings, given in Table 11, have been obtained by actual measurements. 4S. Often it will lie found that, in designing a locomotive cylinder, the space allotted for the steam passages and exhaust passage in the neighborhood of the line c d, iMg. -4, is very small; therefore, great care and good judgment must I e used to ob- tain the proper cross-sectional area in either passage. The result of carelessness right here will be that either one or the other passage is too small, and the engine will fail to do the work that it was intended it should do. STEAM PIPES. 49. Steam pipes, Figs. '24 and L!.">, for locomotives are made of cast-iron; their thickness of metal for smaller engines is about of an inch, and for larger engines about | of an inch. On account of some practical difficulties that must be overcome, ordinary flat joints cannot lie used between the T pipe and the steam pipe, neither between the steam pipe and cylinder saddle. The first difficulty that presents itself is the expansion and contraction due to the great change of temperature to which the steam pipes in locomotives are exposed, and therefore we must adopt a joint which possesses a small amount of flexibility. The second difficulty that presents itself is of a practical nature, namely, the impossibility to construct a boiler and fit the cylinder saddle to the outside of the smoke-box with absolute accuracy, yet a steam pipe of proper length is expected to fit at once iii its place, without any more labor than would be required if everything elm had Keen perfectly accurate; hence, the joint must possess a small amount of adjustability. Adopting a ball joint, the foregoing difficulties can be overcome. These ball joints are made (as shown in Fig. 124) by interposing a brass ring between the T pipe and steam pipe, and another one between the steam pipe and cylinder saddle. Each brass ring has a spherical and a flat surface. Now, it must be readily perceived that with such rings interposed the steam pipe can be slightly moved up or down or sideways, and still maintain a steam-tight joint. This kind of ball joint will also be sufficiently flexible to allow for the contraction and expansion of the steam pipe. PISTON SPEED. 51). To determine the piston speed in feet per minute according to the following rule, we must know the speed of train in miles per hour, the diameter of the driving wheels in feet, and the length of stroke in feet: KYuE 1). To find the piston speed in feet per minute in a locomotive, multiply the number of feet in a mile by the speed of train in miles per hour, divide the product by the circumference in feet of the driving wheel multiplied by (!0, and multiply the quotient by twice the length of the stroke in feet ; the product will be the piston speed in feet per minute. Or, writing this rule in the shape of a formula, we have iXunibiT of fret > \ Spi'i'il nf train in I in ;i mil.- \ ' I mill's JKT lionr \ i piston SIII-IM! ) S nr,.,,,,,f,.r,.,, ...... f .Irivi,,,? wl.,,1 , * twK>| - "'" S "'" k " '" 1 "" t ' / in f,,. ,,,,- min,,.,. * ' 34 MODERN LOCOMOTIVE CONSTRUCTION. EXAMPLE 12. Find the piston speed in feet per minute in a locomotive whose driving wheels are 5 feet in diameter ; stroke, 2 feet ; and speed of train, 35 miles per hour. According to Rule 9, we have 5280 x 35 _ 7 o, fi o 15.7 x 60 X That is, the piston speed will be 784i 6 % feet per minute. In order to assist the reader to understand the foregoing rule, the following explanation is offered : First, we multiply the number of feet in a mile by the speed of train in miles per hour ; this product will give the number of feet the locomotive travels in one hour, and, since there are 5,280 feet in a mile, and the speed of train in our example is 35 miles per hour, we have 5,280 x 35 = 184,800 feet that the locomotive travels during one hour. To find the number of feet that the locomotive travels during one minute, we divide the number of feet per hour by GO, because there are 60 minutes in one hour ; hence, in our example, -^r^ 1 = 3,080 feet ; that is, during one minute the locomotive travels through a distance of 3,080 feet. To find the number of revolutions of the wheel per minute (which is necessary in this case), we divide the distance traveled per minute by the circumference of the driving wheel. In our example, the diameter of the driving wheel is 5 feet ; the circumference of such a wheel is 15.7 feet ; therefore, = 196.17 number of revolutions per minute. During every revolution of the wheel .Lo. t the piston travels through twice the length of the stroke ; therefore, mutiplyiug the number of revolutions per minute by twice the length of the stroke, the piston speed per minute will be obtained. In our example, the stroke is 2 feet; therefore, 196.17 x 4 = 784 j^o f ee t- That is, the piston speed is 784-jVo feet per minute. SLIDE-VALVES, AND MOVEMENT OF SLIDE-VALVES. 51. Slide-valves are sometimes made of brass, but generally of cast-iron. Cast- iron slide-valves are more durable than brass valves, but the latter do not wear the valve's seat as quickly as the cast-iron valves. The ordinary form of slide-valve, such as is generally used in locomotives, is shown in Figs. 26 and 27. Fig. 26 represents a cross-section of the valve ; one-half of Fig. 26 Fi(J , 27 Fig. 28 Fig. 27 shows a section lengthwise of the valve, and the other half an outside view of the same. The thickness of metal at a is generally made 1 in., and at b about i in. The sides c d, e/are extended upwards until they become flush with the top, />, of the valve; in some cases these sides are extended a little beyond the top of the valve. This has been done for the following practical reasons: In the first place, a large Moni':i;\ LOCOMOTIVE cn\firiii'cTro2f. 35 surface is obtained against which the valve yoke can bear. Secondly, this form of valve can be laid on its back, and thus speedily and conveniently secured to the planer, when the valve face is to be planed; this is a matter of no small importance in a large locomotive establishment where a number of valves have to be planed daily. The recesses g g, shown in Fig. 26, are simply for the purpose of making the valve as light as possible. Some master mechanics object to these recesses, because they believe that they will hold the oil (which is usually admitted through the top of the steam chest), and prevent the oil from falling upon the valve seat, and thus not find its way into the cylinder. For this reason a valve has been adopted having a form as shown in Fig. 28. This form of valve, although used on some roads, has not been favorably received on other roads, because it takes up too much room in height, and besides it is an incon- venient casting to fasten to the planer when the face is to be planed or replaned. The writer would recommend the adoption of a valve having a form as shown in Fig. 26, and believes that the fear of the recesses g g preventing the oil from flowing into the cylinder is groundless, and that the constant flow of steam into the chest will not allow the oil to lay still on any part of the valve. T)!'. The duty of the slide-valve is to control the flow of steam into and out of the cylinder, that is, the valve (as its name implies) slides backward and forward on the Yoke Brace Fig.29 Valve Gear for an Eight wheeled, locomotive valvo seat, thus opening and closing the steam ports at proper times. Whether it will perform this duty or not, depends upon the form and motion of the valve. Fig. 29 shows a complete locomotive valve gear; the names of the different pieces of the mechanism are plainly marked on the drawing, so that here any further defini- tions of these pieces will be unnecessary. 53. To construct a slide-valve and assign to it the proper motion, such as shown in Fig. 29, may seem to be a difficult subject for solution; and so it would be, if, ri.dit in the beginning, we do not wheresoever we can throw out of consideration all such pieces of mechanism as have a complicating influence upon the motion of the valve. Hence it is of the utmost importance first to reduce this subject to its simplest form. It will lie noticed that tin- operation of the valve is controlled by two eccentrics : one eccentric is used for the forward motion and the other for the backward motion of tin- engine. Here we may simplify our subject by leaving out of consideration the back- 36 MODERN LOCOMOTIVE CONSTRUCTION. ward eccentric, because when the valve is made to accomplish the desired results with one eccentric its form will not have to be changed when the other eccentric is added. But leaving the backward eccentric out of the question, we may also leave the link out of consideration, because the link only serves to connect the two eccentric-rods so as to enable the engineer to put wholly or partly into gear one or the other eccentric. The lifting-shaft is simply used for moving the link up or down as the case may be ; and since the link has been thrown out of consideration, we may treat the lifting-shaft likewise. The rocker is simply used for the purpose of connecting the eccentric-rod to the valve-rod, and although it affects the position of the eccentrics, and in some cases the travel of the slide-valve, it will not affect the laws relating to the construction of the valve, and therefore we also throw this out of consideration. 54. Reducing our subject as described, and connecting the eccentric-rod directly to valve stem, we obtain a simple arrangement, Fig. 30, such as is often used in stationary B engines; of course, in this arrangement we must assume that the driving axle of the locomotive is represented by the crank shaft C, and the eccentric placed on the end of the shaft as shown. In this arrangement, simple as it is, a feature exists which has a somewhat complicating influence upon the motion of the valve, and therefore will interfere with the simplicity of our study of the laws relating to the form of the valve. The feature alluded to is the angle that the eccentric-rod makes with the center line, A B. This angle varies during the travel of the valve, and consequently the motion of the valve will be slower during one half of the travel than during the other half. Thus, for instance : Let the line A B in Fig. 31 represent the line A B shown in Fig. 30. The circle s l t t u lt Fig. 31, will represent, in an exaggerated manner, the path of Fiy.31 Fig.32 the center x of the eccentric, shown in Fig. 30, and lastly, the distance from the center x to the center t of the eccentric-rod pin in Fig. 30 is represented by the line t l t in Fig. 31. Now, referring only to Fig. 31, when the valve stands in an extreme position of its travel, the center of the eccentric-rod pin will be at , the center of the eccentric will be at M I? and the center line of the eccentric-rod will lie in the line A B. Again, when the valve stands in the other extreme position of its travel, the center of the eccentric-rod pin will be at s, the center of the eccentric will bo at * and the center line of the eccentric-rod will lie in the line A B. When the slide-valve stands central 37 that is, midway between the extreme ends of its travel, the center of tiie eccentric-rod j)in will be nl /, exactly midway l<'t\vt'cii the points \ and it. From the point / as a center, and with a radius equal to the distance C t, describe an an- ; this an- will intersect the circumference *, /, , in the points /, and t.,. Join the points / and /, l>y a straight line, also draw a straight line from the point t to the point (.,; then the straight line / /, or / /., will represent the center of the eccentric-rod when the valve stands in a midway position of its travel; the point t will 1 >e the center of the eccentric-rod pin and the point /,, or the point (._, will he the center of the eccentric. Assume that the shaft is turning in the direction indicated by the arrow. When the eccentric-rod pin has traveled from n to /, equal to half the travel, the slide-valve has also completed one-half of its travel, and the center of the eccentric has traveled through the arc n l /,. Again, during the time that the eccentric-rod pin travels from t to N, equal to half the travel, the center of the eccentric will travel through the arc t l Sj. lint now notice the difference of length of the two arcs t l s } and t } >i t ; this plainly shows that the eccentric-rod pin will travel slower from M to / than from t to s, and consequently the travel of the valve will be affected likewise. Or, we may say, that the angle formed by the lines / /,, and ./ // destroys the symmetry of the valve motion. Now, in the study of the laws relating to the motion of the valve and the duties it has to pel-form, such a motion will complicate matters, and will prevent us from tracing the action of the valve so readily as when both halves of the travel are described in equal times, and therefore the reader will perceive the necessity of changing the valve gear to one which will give the valve a perfectly symmetrical motion. In the first place, it will be easily seen that the longer we make the eccentric-rod leaving the travel of the valve the same the smaller will be the angle between the line / /, (which represents the center of eccentric-rod), and the line A B, and conse- quently the times in which the halves of the travel of the valve are described will be nearer equal, and when we assume the eccentric-rod to be of an infinite length the angle will vanish and each half of the travel of the valve will be described in equal times, and the motion will be symmetrical; in fact, the valve will have precisely the same motion as that obtained with a valve gear, as shown in Fig. 32, to which we shall now call attention. '>'>. In this tigure, in place of using an eccentric-rod, the valve-stem is lengthened, and to its end a slotted cross-head is forged. The eccentric has also been dispensed with, and in its place a pin // fastened into the end of the crank-shaft has been adopted. The distance between the center (' of the crank-shaft and the center of the pin // must always be equal to the distance between th nter ('and the center x of the eccentric shown in Fig. oil. This distance from (' to ./ is called the eccentricity of the eccentric, and is equal to one-half of the throw, or in other words the throw of an eccentric is equal to twice its eccentricity. In this particular case, as shown in Fig. :>0, the throw is equal to the travel of the valve; by the travel of the valve is meant the distance between the extreme points of its motion. In all direct acting valve motions, that is when no rocker or link is used, the throw of the eccentric will be equal to the travel of the valve. In locomotives, the travel of the valve is not always equal to the throw of th centric, the difference being due to the inlluence of the link, and often to the unequal length of the rocker-arms. 38 MODERN LOCOMOTIVE CONSTRUCTION. ralty Seat /Path of the centre of the eccentric (nee Fig 30) Now, turning our attention to Fig. 32, we notice that by substituting for the eccentric a pin y in the end of the crank-shaft, we really adopt a crank, and this we can do without affecting the correctness of the reasoning relating to the movement of the valve, because the action of the eccentric is precisely the same as that of a crank whose length is equal to half the throw ; the only reason why eccentrics are adopted is that they are more convenient to use ; in fact, cranks in many cases cannot be used, the peculiar construction of the machine preventing their adoption ; in no case is an eccentric adopted because a different motion to that due to a crank is desired. We have drawn particular attention to this fact, because some mechanics (a good many of them) have a misty notion of the action of an eccentric. As the shaft revolves (see Fig. 32) the pin in the end of the shaft will move in the slot of valve-stem's cross-head, and thus always allowing the center line of the valve- stem to coincide with the line A B. It must also be plain that as the shaft revolves the center of the pin will describe a circle, and it is the circumference of this circle that will enter into the solutions of the fol- lowing problems. Once more, the reader will readily perceive that the length of the valve-stem will in no Dtameter of thU circle- travel of ttemlve. WiS6 affect the motion Of the ValVB, hence we may leave this also out of consideration, and place the circumference of the circle which represents the path of the pin y on the end of the slide-valve, as shown in Fig. 33. Here, then, we notice that our original subject, that of finding the proper motion and form of a valve, a subject in which all the different pieces of mechanism as shown in Fig. 29 had entered, has been reduced and simplified to that having only the pieces of mechanism as shown in Fig. 33. THKEE CONDITIONS A SLIDE-VALVE MUST FULFILL. 56. The entrance of steam into the cylinder is regulated by the two outside edges, a ft and c d, of the slide-valve, Fig. 34 ; the exit of the steam is regulated by the two inner edges, efandg h, of the slide-valve; and the correct admission and exhaust of the steam depends upon these edges, the motion of the valve that is, the travel of the valve and the position of the eccentric. All slide-valves must be capable of fulfilling the three following conditions, and if a slide-valve cannot do this, the engine will not work satisfactorily : First Condition. Steam must be admitted into the cylinder at one of its ends only at one time. To satisfy this condition, the length of the valve from a to c must at least cover both steam ports, when the valve stands in a central position, as shown in Fig. 34. This length of the valve cannot be less, because if it is made less, steam will enter both ends of the cylinder at one time, and consequently bad results will follow. Second Coi////tiii. The valve must allow the steam to escape from one end of the cylinder, at least as soon as it is admitted into the other end of the cylinder. To fulfill I.O<-OM<>TI\ /: 39 this second condition, the length of the exhaust cavity in the valve, or, in other words, the distance between the two inner edges, efanAg //, Fig. 34, must be equal to the sum of t lie widths of the two bridges added to the width of the exhaust port. The length of the exhaust cavity in a valve whose outside edges just cover the steam ports, must not lie made less than shown in Fig. 34, because if it is made less, steam will be ad- mitted into one end of the cylinder, some time before the steam in the other end of the cylinder is released, and consequently a considerable amount of back pressure will be the result. When the outer edges of a valve overlap the steam ports, such as shown in Fig. :!<>, then its exhaust cavity can be made less, within certain limits, and still satisfy the second condition. Tlni-il Cnndititiii. The valve must cover the steam ports so as not to allow the steam to escape fi'oin the steam chest into the exhaust port. To fulfill the third con- Fi y. 3 Fid- 35 fig. 36 dition, the length of the exhaust cavity, that is, the distance between the edges e and g, Fig. 34, must not be made greater than the sum of the width of the two bridges added to the width of the exhaust port, in a valve whose outside edges just cover the steam ports. If the length of the exhaust cavity in such a valve is made greater, then the distance between the edges a and e, or the distance between the edges g and c will be less than the width of steam ports, and consequently the steam will be permitted to pass from the steam chest directly into the exhaust port, as indicated in Fig. 35, or, as the practical man would say, the steam will blow through, and therefore an unpardon- able waste of steam will be the result. If the outside edges of the valve overlap the steam ports, as shown in Fig. 36, then the exhaust cavity can be made within certain limits a little longer, without interfering with the third condition. 57. For the sake of distinction we may divide slide-valves into two classes. In one class we may place all slide-valves whose outside edges just cover the steam ports, such as shown in Fig. 34. These valves will admit steam into the cylinder during the whole stroke of the piston, or, as the practical man would say, " the valve follows full stroke." In the other class we may place all slide-valves whose outer edges overlap the steam ports, such as shown in Fig. 36. These valves will not admit steam into the cylinder during the whole stroke of the piston, but will close the steam ports, and thus cut off the flow of the steam into the cylinder, before the piston has reached the end of a stroke. The position of the piston at the moment that steam is cut off is called the point of cut-off, and this point depends upon the amount of lap. ."is. When a valve of this kind is placed in a central position, that is, midway of its travel, as shown in Fig. .'!>, then the amount of overlap at each end is called "outside 40 MODERN LOCOMOTIVE CONSTRUCTION. lap," or simply lap. Thus, if as in Fig. 36, the valve overlaps each port | of an inch, then the valve is said to have J of an inch lap. Under no circumstances should one of the outside edges of the valve be placed flush with an outside edge of the steam port, and then the total amount of overlap at the other end of the valve be called lap, because that would be wrong according to the universal acceptation of the term " lap." TRAVEL OF THE VALVE. 59. Since it is always taken for granted that the steam ports are made just large enough and no more to give a free exhaust, we must give the valves that have no lap, as shown in Fig. 34, such a travel that the outside edges of these valves will wholly open the steam ports. We cannot make this travel any less, because if it is less the steam port will not be fully open to the action of the exhaust. On the other hand, theoretically, the travel of a valve that has lap need not be such that the steam port will be fully opened to the admission of steam ; all that is really needed for this pur- pose is an opening of ^ of the width of the steam port, and if this does not interfere with the free action of the exhaiist, that is, if it does not prevent the full opening of the steam port for the escape of steam, satisfactory results will follow. In practice, such niceness in the travel of the valve is seldom aimed at. In fact, it is customary to assign such a travel to a valve that the outside edges of the valve will not only fully open the steam ports, but travel a little beyond them. Adopting such a practice, we gain the following advantages : When a valve that has no lap travels a little further than necessary to fully open the steam port, we have the assurance that a slight inaccuracy in workmanship, which cannot always be prevented, will not interfere with the full opening of the steam port. Again, it is always desirable that when the valve is to cut off steam, it will do so as quickly as possible, hence, when valves that have lap and their travel is greater than absolutely necessary, the motion of these valves will be quicker than the motion of valves with shorter travel ; therefore, when the former are employed, the cut-off will be sharper and more decisive. EXAMPLE 13. To find the travel of a valve that has no lap, the width of the steam port being given, let the steam port be li inch wide. The travel of a valve without lap must at least be equal to twice the width of the steam port. The truth of this must be perceived when we examine Fig. 34, and remember the remarks just made. Consequently the travel of the valve in our example will be li x 2 = 2J". From the foregoing we may establish the following : RULE 10. To find the travel of a valve without lap, the steam port to be fully opened and no more. Multiply the width of steam port in inches by 2, the product will be the travel of the valve. Now, if the travel of the valve is to be such that the valve shall move i of an inch beyond the steam port, then we must add this amount to the width of steam port, and make the travel equal to twice this sum. Thus : EXAMPLE 14. Width of steam port li inch, the valve to .travel i of an inch beyond the steam port, find the travel, li + i == li, and li x 2 = 3 inches = travel of the valve. From the foregoing we have the following : RULE 11. To find the travel of the valve without lap, the travel to extend a given .MIIHKK\ Loco.tiDT/1-K ro.v.STV.vrTW.v. 41 amount beyond the steam port Add the given amount which the valve must travel beyond tlic steam port to the width of the steam port, multiply the sum by 2; the product will lie the travel of the valve. (iO. When this valve is used in an engine with no rocker interposed, then the eccentricity of ill -centric, or, in other words, the distance between the center, f, of the crankshaft and the center, ./, of the eccentric, Fig. 30, will be li inch, and the throw of the eccentric will be equal to the travel of the valve, namely, 3 inches. To iii n 1 tin 1 travel of a valve that has lap, the lap and width of the steam port being given : I'AAMI'LE 1"). The width of the steam port is lj inch, the lap is J of an inch, find the travel. If the valve is to open the steam port fully, and no more, for the admission of steam, then the travel cannot be less than twice the sum of the width of the steam port and lap. Hence in our example we have 1J + J = 2j, and 2J x 2 = 4\ inches = travel of the valve. If the valve is to move J of an inch beyond the steam port, then we have M + J + I 28, and 2g x 2 = 4f inches = travel of the valve. When no rocker is inter- posed, the throw of the eccentric is equal to the travel, that is, 4 inches. From the foregoing we can establish the follow rules: Kn,E 1 To find the travel t if the valve with lap, the travel not to extend beyond the steam port. Add the width of the steam port to the lap, multiply the sum by 2; the product will be the travel of the valve. RULE 13. To find the travel of a valve with lap, the travel to extend beyond the steam port. Add the width of the steam port, the lap, and the amount of travel beyond the steam port, multiply this sum by 2; the product will be the travel of the valve. POSITION OF ECCENTRIC WHEN NO EOCKEK IS USED. 61. Assume that a valve without lap is to be used in an engine similar to that shown in Fig. 37, that is, an engine in which the axis of the cylinder will pass through the center of the crank-shaft ; also let it be required that at the precise moment at Backcnd /'if/. - =XJL a Front end which the piston readies the end of a stroke, the valve shall open the steam port. In Fig. 37, it will be noticed, that instead of showing the back of the slide-valve as it should be, we have assumed the valve and seat to be turned around the valve stem, SO as to see a section of the valve ;md seat : this will make the illustration more intelligible for our purpose. Now, assume that the piston stands at I), the back end of the stroke, then the crank will be in the position as shown, and according to our proposition, the 42 MODERN LOCOMOTIVE CONSTRUCTION. valve must at that instant open the back stearn port, consequently the valve must stand in the position as indicated in the figure. Again, assume that the piston stands at E, the front end of the stroke, then the valve must stand in a position so that the least movement will open the front steam port, consequently the valve will occupy the same position as before. In fact, when the piston stands at either end of the stroke, the valve, having no lap, must stand in a central position, that is, midway of its travel. To find the suitable position of the eccentric when this valve stands central, we proceed as follows : From the center C describe a circle a b d (Fig 37), whose diameter is equal to the travel of the valve ; the circumference of this circle will represent the path of the center of the eccentric, or, what amounts to the same thing, the path of the center of the pin y ; consequently the exact location of the center of this pin must be found somewhere in the circumference a b d. Now, the diameter a b is equal to the travel of the valve, hence we may assume that the point a will represent one end, and the point b the other end of the travel, and C the center of the travel. Therefore to find the location of the pin y, draw through the center C a line i h perpendicular to the line A B ; the line i h will intersect the circumference a I d in the points y and d. If the crank-pin is to turn in the direction of the arrow marked 1, then the point y will be the center of the pin or the center of the eccentric ; if the crank is to turn jn an opposite direction, as indicated by arrow 2, then the point d will be the location of the pin y. From the foregoing we learn that the center of the eccentric, or the pin y, will always travel ahead of the crank in either direction, providing no rocker is used. Secondly, we learn that for a valve without lap the center of the eccentric will be found in a line drawn perpendicular to a line passing through the center of crank-pin and the center of crank-shaft, providing the valve has no lead. The straight line drawn through the center of crank-shaft and center of crank-pin will, in the future, be called " the center Vine of crank." 62. By " lead " is meant the width of the opening of the steam port at the com- mencement of the stroke of the piston. Thus, in Fig. 38, when the piston stands at the beginning of the stroke, and the valve has then opened the steam port ^ of an inch, that r c of an inch of opening is called " lead," and the valve is said to have iV of an inch lead. Again, if the valve has opened the steam port & of an inch, instead of -,-',( of an inch, the valve is said to have & of an inch lead. In our previous example the valve l.r<niiiTirK COXSTIU < ri".\. 43 had no lf:i<l, therefore tin- <|uestion arises, where shall we place the eccentric when the valve IIMS li-adf K\\Mi'i,K Iti. Let A l>, in Fig. 39, represent the center line of crank; the direction in which the crank is to move is indicated by the arrow. The lead is to be ^ of an inrh, the travel of the valve 5 inches; find the position of the eccentric. From the center (' draw a circle a b <l, whose diameter is equal to the travel of the valve, namely, '> indies; on the lino A li lay off a point/ / of an inch from the center C; through the point /draw a line k I perpendicular to the line A li, this line k I will intersect the circumference a b d in the points y and rf; the point y will be the center of the eccentric. If tin- crank had been designed to move in the opposite direction, then tin- point (/would have been the center of the eccentric. If no lead had been required, then the center of the eccentric would have been found in the line i h drawn through the center C. From this we learn that when the valve is to have lead the center of the eccentric must lie moved forward of the line * A, and the amount that the center of the eccentric must be moved forward (or away from the crank-pin) is equal to the lead. 63. The line i h is an important one, because the position of the eccentric is always laid off from this line. In this particular case, Fig. 39, the line i h has been drawn perpendicular to the center line of crank. But from this we must not conclude that in every case the line i h must be drawn perpendicular to the center line of crank. The line /' h in every case is drawn perpendicular to the center line of motion of the valve gear, irrespective of the position of the crank. In Fig. 39 the center line of motion of the valve gear coincides with the center line of crank, and it is for this reason that the line i h has been drawn perpendicular to the latter. This will be made plainer as we pro- ceed. By " the center line of motion of the valve gear " is meant a line drawn through the center of the shaft parallel to the direction in which the valve' moves when no rocker or other mechanism between the shaft and valve is used. The definition of the center line of the motion of the valve gear in cases where rockers are used will be given later. TO FIND THE POSITION OF THE ECCENTRIC CORRESPONDING TO ANY ONE OF THE DIFFERENT POSITIONS OF THE VALVE. 64. We have stated in Art. 55, that for the construction of a slide-valve and for the purpose of following the movements of the same, all that will be required is a section of the valve, the valve seat, and the circumference of a circle to represent the path of the center of eccentric, and such we shall now employ in the solution of the following problems. By the center of ec- centric we mean the cen- ter x, Fig. 40, and not the center c of the hole. The center line of MII ec- \^_^/ Fiy.4:l rnj.40 centric is a straight line drawn through the centers / and ', and produced to the circumference of the eccentric Fig. 41 shows the valve seat with the steam ports and exhaust port, also the valve 44 MODERN LOCOMOTIVE CONSTRUCTION. standing in the center of its travel. This position of the valve is an important one, because to this we generally refer when any other position of the valve is to be con- sidered. From the point c (the intersection of the lines A B and d c) as a center and a radius equal to half the throw of the eccentric, a circle has been drawn ; the circum- ference of this circle will represent the path of the center x of the eccentric. Now, it must be remembered that in studying the laws relating to the construction mid move- ment of the slide-valve, the length of the eccentric rod is always considered to be an infinite length, or, in other words, that the eccentric acts precisely in the same man- ner as a pin working in a slotted cross-head forged to the valve stem, such as we have described in Arts. 54 and 61. Keeping this in mind, the following explanation will be easily understood : Since the circumference a I m, Fig. 41, represents the path of the center of the eccentric, it must be readily perceived that the center c of this circle also represents the center of the shaft, and since the line A B is drawn through the center of the shaft, we may call it the center line of motion of the valve gear, because in this particular case the line A B is parallel to the direction of motion of the valve. The diameter a b of the circle a l> m coincides with the line of motion A B, consequently when the center of the eccentric is at b the valve will be at the forward end of its travel, as shown in dotted lines, and at the same time indicating how far the valve will travel beyond the edge of the steam port. When the center of the eccentric is at a, the valve will then stand at the opposite end of its travel, also shown by dotted lines. Now, when the valve stands in its central -position, the center of the eccentric must also stand in the center of its path from a to b, and consequently will be at m. To find the point m we draw a straight line c h through the center c of the circle, and perpendicular to the line of motion A B, the point of intersection of the line c Ji and the circumference will be the point m. ' So also in a similar manner we may find the position of the center of the eccentric for any other position of the valve. For instance, if the edge c of the valve stands at ,9, we draw through the point // a line perpendicular to the line A B ; the point of intersection n of this line and the circumference a b m will be the center of the eccentric, when the valve stands at g. In order to save time and labor, and to make the solutions of the problems as simple as possible, it is always best to place the valve, as we have done, in the center of its travel, and then adopt c, the point of contact of the outer edge of the valve and the valve seat as the center of the circle whose circumference is to represent the path of the center of eccentric. By adopting the foregoing suggestion we also gain the following advantages ; namely, we can see at once how far the valve will travel beyond the steam port in either direction; and we can also see how much the exhaust port will be contracted when the valve is at end of its travel. Hence it must be distinctly remembered that to trace the motion of any slide-valve, the valve should lie placed in a central position, and the center of circle whose circumference represents the path of the center of the eccentric should be the point in which one of the outer edges of the valve touches the valve seat. \inni:i;.\ <-<>.\xn:rrri<>.\ 45 I.1M.AK ADVANCE OF THE VALVE AND ANGULAR ADVANCE OF THE ECCENTHIC. (i.">. In connection witli tin 1 setting of the eccentric two terms ai - e used, namely, "lin- ear advance <>t' tin- valve" and "angular advance of the eccentric." Between these two there exists sueh a close relation that if we change one we must also change the other, and it' there is no linear advance of the valve there will be no angular advance of the eccentric, therefore it is of great importance to understand the meaning of these terms. In Fig. 4'2 we have shown the valve in two positions. The dotted lines represent the valve standing in the center of its travel, and is marked D. The section of the valve in t'ull lines, marked E, represents its position at the commencement of the /. ; / Fig.44 Fig.45 stroke of the piston (it will be noticed here that the valve has lead), the distance from c to r, is called linear advance of the valve, and is equal to the lap and lead, plainly shown in the figure; in short, linear advance of the valve means the distance the valve has traveled beyond its middle position when the piston has reached the end of the stroke. When the valve stands in the middle position D, the center of the eccentric. will be at ///, and a line drawn from c to m will represent the center line of the eccentric. Again, when the valve stands at ', the center of the eccentric will be at y, and a line drawn from c to y will again represent the center line of the eccentric. The angle formed by the lines c m and c y is called the angular advance of the eccentric; or, in other words, by angular advance is meant the angle that is formed by the position of the center line of the eccentric when the piston is at the commencement of the stroke, and the position of the center line of the eccentric when the valve is in the center of its travel, the length of the eccentric rod being assumed to be infinite. tiii. If the lap is increased without changing the travel and lead, as shown in Fig. 4.'!, the linear advance will be greater, and consequently the angular advance m c y will also lie increased, which is plainly indicated in the figure. Here also notice that the center r has been moved away from the outside edge of the steam port, because when the valve is placed central, its outside edge r, will be at r, which, according to what has been stated before, should be adopted for the center of the circle, whose circum- ference (i in l> represents the path of the center of the eccentric. I>y so doini;, we see at a glance how far in either direction the valve will travel. In this figure we notice that the valve does not travel as far beyond the inner edge of the steam port as in Fig. 42. 46 MODERN LOCOMOTIVE CONSTRUCTION, If the lap is made less than shown in Fig. 42, without changing the travel and the lead of the valve, the linear advance will be less, and consequently the angular advance will be smaller. In this particular case the center c would have to be moved closer to the edge of the steam port, because the lap is smaller. When the valve has no lap and lead, as shown in Fig. 44, there will be no linear advance, and consequently no angular advance. In this case the center c will be on the outer edge of the steam port. If the travel of the valve is the same as that in Fig. 43, and indicated by the diameter of the dotted circle a m b in Fig. 44, we notice that in the latter figure the travel is too great ; our circle shows that the valve will travel beyond the bridge, and thus open the exhaust port to the steam in the steam chest; therefore, the travel must be reduced, as shown by the circumference % m l I in a full line. Lastly, if lead be given to a valve that has no lap, as shown in Fig. 45, then we have again linear advance, and conse- quently there will be a corresponding amount of angular advance. In this case the center c will remain on the outside edge of the steam port. TO FIND THE KELATIVE POSITION OF THE ECCENTKIC TO THAT OF THE CRANK. 67. In Art. 61 it was shown how to set an eccentric for a valve without lap and lead. In that particular example the center line of the eccentric was placed perpendicular to the center line of crank. These relative positions are only true for engines in which all the connections are direct, such as shown in Fig. 30 (see Art. 63). When other connections are used, such as rockers, etc., it may happen that for some engines the eccentric would have to be set at right angles to the crank, or, as the practical man would say, " the eccentric set square with the crank," and yet for other engines this would be wrong. Here we will consider only the relative position of eccentric to that of the crank in simple engines such as represented by Fig. 30. The position of the valve in Fig. 45 indicates that the piston stands at the com- mencement of its stroke, because the small opening of steam port there shown is sup- posed to be lead and no more. Now, assume that the point c is not only the center of the circle whose circumference represents the path of the center of eccentric, but is also the center of the crank-shaft, consequently the center line of crank must pass through c, and since all the connections between crank-shaft and cylinder are direct, the center line of crank must coincide with the line A B. Again, the valve has opened the left- hand steam port, therefore the center P of the crank-pin must also be on the left-hand side of c, and in the line A B. Lastly, the point y is the center of the eccentric, and since the eccentric must travel ahead of the crank (Art. 61) in this class of engines, we conclude that the crank is designed to turn in the direction as indicated by the arrow. In a similar manner, and for similar reasons, it can be proved that when the small openings of the steam ports, as shown in Figs. 42 and 43, represent lead, then the crank-pin P must occupy the position shown in these figures. Notice now the fact that in all the Figs. 42, 43, and 45, the center line c m is per- pendicular to the center line of crank P c, and the angular advance is laid off from the line c m towards the right (away from the crank-pin). Also notice another important fact ; the distance between the lines c m and c : y in all these figures is equal to the M< HI KI; 1: i.\ s //. i 'i n<>.\. 47 linear advance; therefore in order to find the point y we must lay off the linear advance on a line perpendicular to the line c w, and not on the arc tii //. These facts are principles which are applicable to every-day practice. For instance : ('A \MPI.E 17. Travel of the valve is 5 inches, lap 1 inch, lead fa of an inch, and the direction in which the crank is to move is indicated by the arrow, Fig. 40. Find the relative position of the eccentric to that of the crank. I >raw the straight line A B as in Fig. 46, let the point P on the line A B represent the center of the crank-pin, and the point c on the same line represent the center of the shaft. From c as a center, and with a radius equal to 2 inches (which is half the Fig.47 throw of the eccentric), draw a circle a b w, the circumference of this circle will repre- sent the path of the center of the eccentric. From c lay off towards the right a point Cj Ifa inch from c (this I fa inch is the sum of the lap and lead), through c, draw a line r, HI i perpendicular to A 7?, this line c l m l will intersect the circumference a b m in the point //, and this point will be the center of the eccentric when the crank occupies the position as shown. Through the point c draw a line perpendicular to A /?, also a line through the points c and y, then the angle m c y will be the angular advance, and the distance from c to ^ the linear advance. These principles are also applicable to shop practice. KXVMPLE 18. Fig. 40 represents an eccentric; Fig. 47, a crank; Fig. 48, the end of a crank-shaft. It is required to fasten to the crank-shaft the crank and eccentric in their correct relative positions before the shaft is placed in its bear- ings. The lap of the valve is | of an inch, and the lead -fa of an inch. We must first find the half-throw of the eccentric. In this case, see Fig. 40, the diameter of the shaft being greater than the throw of the eccentric, we must force a strip of wood in the hole of the eccen- tric, and on this strip find the center c of the hole, and the center x of the eccentric ; the distance between c and x is equal to half the throw. Through c and x draw a straight line c g ; this line will be recognized as the center line of the eccentric. Fig. 47. On the face of the crank draw through the centers c and P a straight line, which will be the center line of crank. Fig. 48. Through the center c of the shaft draw any straight line, as /'_, /'.. From the center r, and with a radius equal to half the throw of the eccentric, draw <>n the end of the shaft a circle (/ I/ HI. On the line /'._, /'., lay off a point r L , j ;': of an inch from the center c; through the point t:, draw a straight line perpendicular to /'_, /'.,, J'.nit nfaliii/'l Fiij.48 48 MODERN LOCOMOTIVE COXSTllt'CTlOX. intersecting tho circumference a b m in the point y; through the points c and i/ draw the straight line c y 2 . Fig. 49. Place the crank on the shaft so that its center line P c will coincide with P 2 c on the shaft, and then fasten the crank. Place the eccentric on the shaft so that its center line g c will coincide with c y., on the shaft, and fasten the eccentric. The crank and eccentric will then have the correct position on the shaft, and must not be changed for a valve having & of an inch lap and -fa of an inch lead. We here Fiff.49 F'uj.50 End f .thrift Firj.51 again call the attention of the reader to the fact that these relative positions of crank and eccentric are only correct for engines in which all the connections are direct, and in which no rocker is used. When it is necessary to place the crank and the eccentric some distance from the end of the shaft, it will be an easy matter to draw on the outside of the shaft lines through the points P 2 and y., parallel to the axis of the shaft, and then set the crank and eccentric; to these lines. Should it so happen that the throw of the eccentric is larger than the diameter of the shaft (but which seldom occurs), draw on paper or on a board any straight line a b, as in Fig. 50, and from a point C on this line as a center, and with a radius equal to half the throw of the eccentric, draw the circle a b m. Find the point y in the circum- ference a b m in the same manner as the point y in Fig. 46 has been found, and then draw the lines m C and y C. From the center (7, and with a radius equal to half the diameter of the shaft, draw the circle P 2 P 3 , whose circumference will intersect the straight lines m C and y C in the points w ;) and y 3 . Through the center c of the shaft, see Fig. 51, draw a straight line P 2 P 3 , and also the line m. 2 c perpendicular to P 2 P :J ; make the arc m. 2 y. 2 equal to >n 3 y. A in Fig. 50 ; draw on the end of the shaft the line y. 2 c ; set the eccentric to the line y. 2 c, and the crank to the line c P 2 . THE EFFECT OF LAP. 68. When only one slide-valve is used for the whole distribution of steam in one cylinder, as in locomotives, and the valve has no lap, we may justly name the form of such a valve a primitive one, because valves without lap, or with only a trifling amount, about fa of an inch, were used in locomotives years ago, when the great neces- sity for an parly and liberal exhaustion was not so well understood as at present, the chief aim then being to secure a timely and free admission of steam. Such valves, as -:H\ i.i>ct>Mt>TirK i-(>\sri;rcrii>\. 49 we have stated before, will admit steam during the whole length of the stroke, or, in other words, follow full stroke, and release the steam in one end of the cylinder at the same moment, or nearly so, that the steam is admitted into the other end; this is cer- tainly no profitable way of using stearn, for the following reason: The process of exhausting steam requires time, and therefore the release of steam should begin in one end of the cylinder some time before steam is admitted into the other end, or, we may say, the steam which is pushing the piston ahead should be released before the end of the stroke has been reached. This cannot be accomplished with a valve having no la}), and consequently, when such a valve is used, there will not lie suflicient time for the exhaustion of steam, thus causing considerable back pressure in the cylinder. In order then to secure an early exhaust, lap was introduced ; first, of an inch lap was adopted, then of an inch. But it soon became apparent that working the steam expansively (a result of lap, besides gaining an early exhaust) addi- tioiial economy in fuel was obtained, hence the lap was again increased until it became 5 of an inch, and in some cases 1 inch, and even more than this. At the present time the lap of a valve in ordinary locomotives with 17" x 24", or 18" x 24" cylinders is J to 1 inch, and in a few cases slightly exceeding this. From these remarks we may justly conclude that in these days the purpose of giving lap to the valve is to cause it to cut off steam at certain parts of the stroke of the piston, so that during the remaining portion of the stroke the piston is moved by the expansion of the steam. When steam is used in this manner, it is said to be used expansively. Now, since the aim of giving lap to a valve, is to cause it to cut off steam at desig- nated parts of the stroke of the piston, it will be necessary first to study the existing relation between the motion of the crank-pin and the motion of the piston. RELATION BETWEEN MOTION OF CRANK-PIN AND MOTION OF PISTON. 69. In order to illustrate this subject plainly, we have adopted in Fig. 52 a shorter length for the connecting rod than is used in locomotives. The circumference of the circle A B M I), drawn from the center of the axle, and with a radius equal to the distance between the center of axle and that of the crank- pin, represents the path of the latter. We will assume that the motion of the crank- pin is uniform, that is, that it will pass through equal spaces in equal times. The direction in which the crank-pin moves is indicated by the arrow marked 1, and the direction in which the piston moves is indicated by arrow 2. In order to trace the motion of the piston it is not necessary to show the piston in our illustration, because the connection between the cross-head pin P and the piston is rigid ; hence, if we know the motion of the former, we also know the motion of the latter. The line A C represents the line of motion of the center of cross-head pin P, con- sequently no matter what position the crank may occupy, the center P will always be found in the line A. C. The semi-circumference A li I) will be the path of the center of the crank-pin P during one stroke of the piston; the point A will be the position of the crank at the beginning of the stroke; and //, the position of the same at the end of the stroke. The semi-circumference A B D is divided into 12 equal parts, although 50 MODERN LOCOMQTirE COXST&VOffOJT. any other number would serve our purpose as well. The distance between the centers D and P represents the length of the connecting-rod. From the point A as a center, and with a radius equal to D P (the length of the connecting-rod), an arc has been drawn, cutting the line A Cin the point a; this point is the position of the center P of the cross-head pin, when the center of the crank is at A. Again, from the point 1 on the semi-circumference as a center and with the radius D P, another arc has been drawn cutting the line A C in the point Ip, and this point indicates the position of the cross-head pin when the crank-pin is at the point 1. In a similar manner the points 2p, 3p, 4p, etc., have been obtained, and these points indi- cate the various positions of cross-head pin when the crank-pin is in the corresponding positions, as 2, 3, 4, etc. Now notice the fact that the spaces from A to 1 and from 1 to 2, etc., in the semi- circumference A B D are all equal, and the crank-pin moves through each of these spaces in equal times, that is, if it requires one second to move from A to 1, it will also require one second to move from 1 to 2. The corresponding spaces from a to Ip and from Ip to 2p, etc., on the line A C are not equal, and yet the cross-head pin must move through these spaces in equal times ; if it requires one second to move from a to Ip, it will also require one second to move from Ip to 1p. But this last space is greater than the first. Here, then, we see that the cross-head pin, and therefore the piston, has a variable motion, that is, the piston will, at the commencement of its stroke, move comparatively slow, and increase in speed as it approaches the center of the stroke, and when the piston is moving away from the center of stroke, its speed is con- stantly decreasing. This variable motion of the piston is mostly caused by changing a rectilinear motion into a uniform rotary motion, and partly by the angle formed by the center line D P of the connecting-rod and the line A C, an angle which is con- stantly changing during the stroke. Also notice that the distance from a to Ip nearest one end of the stroke is smaller than the distance from b to lip nearest the other end of the stroke, and if we compare the next space Ip to 2p with the space Up to IQp, we again find that the former is smaller than the latter, and by further comparison we find that all the spaces from a to 6p are smaller than the corresponding spaces from b to 6p, and consequently when the crank-pin is at point 6, which is the center of the path of the crank-pin during one stroke, the cross-head pin P will be at 6p, and not in the center of its sti'oke. Thus we see that the motion of the piston is not symmetrical, and this is wholly due to the varying angularity of the connecting-rod during the stroke. If we make the connecting-rod longer, but leave the stroke the same, the difference between the spaces b to lip and a to Ip will be less, and the same can be said of the other spaces. Again, if we consider the length of the connecting-rod to be infinite, then the difference between the spaces nearest the ends of the stroke will vanish, and the same result is true for the other spaces. Hence, when the length of the connect- ing-rod is assumed to be infinite, the motion of the piston will be symmetrical, but still remain variable ; in fact, the piston will haveithe same motion as that shown in Fig. 53. In this figure we have dispensed with the connecting-rod, and in its place extended the piston rod, and attached to its end a slotted cross-head in which the crank-pin is to work. Although such mechanism is never used in a locomotive, yet with its aid we can establish a simple method for finding the position of the piston when that of the MODKK.\ LOCOMUl'lfK (OXtiTRUCTION. 51 crank is known. In this figure, as in Fig. 52, the circumference A B D M will repre- sent the path of the center of the crank-pin, and from the nature of this mechanism it must be evident that at whatever point in the circumference A B D M the crank-pin center may lie located, the center line i h of the slotted cross-head will always stand perpendicular to the line A 6', and also pass through the center of crank-pin. In Fig. 5:!, when the crank-pin is at A, the piston will be at the commencement of its stroke. During the time the crank-pin travels from A to point 8 the piston will travel through a portion of its stroke equal to the length A E, which is the distance between the dotted line i h and the full line i h. If now we assume the points 1, 2, 3, etc., in the semi-circumference A B I) to be the various positions of the crank-pin dur- ing one stroke, and then draw through these points lines perpendicular to the line A C, cutting the latter in the points 1p t 2p, 3p, etc., we obtain corresponding points for the fig. 54 position of the piston in the cylinder. Thus, for instance, when the crank-pin is at point 1, the piston will then have moved from the commencement of its stroke through a distance equal to A lj>, and when the crank-pin is at point 2, the piston will then have traveled from A to '2/>, and so on. 70. From the fort-going, wt- can establish a simple method, as shown in Fig. 54, for finding the position of the piston when that of the crank is known. The diameter A II re]. resents the stroke of the piston, and the semi-circumference A B 1) represents the path of the center of the crank-pin during one stroke. For convenience, we may 52 MODEHN LOCOMOTIVE CONSTRUCTION. divide the diameter into an equal number of parts, each division indicating one inch of the stroke. In this particular case (Fig. 54), we have assumed the stroke to be 24 inches ; hence the diameter has been divided into 24 equal parts. Let the arrow indi- cate the direction in which the crank is to turn, and A the beginning of the stroke ; then, to find the distance through which the piston must travel from the commence- ment of its stroke during the time, that the crank travels from A to b, we simply draw through the point b a straight line 7; c perpendicular to A B ; the distance between the line b c and the point A will be that portion of the stroke through which the piston has traveled, when crank-pin has reached the point b. In our figure we notice that the line b c intersects A B in the point 6 ; hence the piston has traveled six inches from the commencement of the stroke. If this method of finding the position of the piston when that of the crank is known is thoroughly understood, then the solutions of the following problems relating to lap of the slide valve will be comparatively easy. PBOBLEMS RELATING TO LAP OF THE SLIDE-VALVE. 71. To find the point of cut-off when the lap and travel of the valve are given, the valve to have no lead. The principles upon which the following problems relating to the construction of the slide-valve are based, have been taken from the excellent " Practical Treatise on the Movement of Slide- Valves by Eccentrics," by Prof. C W. MacCord. EXAMPLE 19. Lap of valve is one inch; travel, 5 inches; no lead; stroke of piston, 24 inches. At what part of the stroke will the steam be cut off ? We must first find the center c, Fig. 55, of the circle a b m, whose circumference represents the path of the center of eccentric, and this is found, as the reader will re- ] member, by placing the valve in a central position (Art. 64), as shown in dotted lines in this figure. Then the edge c of the valve will be the center of the circle. The valve drawn in full lines shows its position at the commencement of the stroke of piston ; and since the valve is to have no lead, the edge Cz will coincide with the outer edge of the steam port. Through the edge 2 draw the line i h perpendicular to the line A B ; the line i h will intersect the circumference a b m in the point y, and this point will be the center of eccentric when the piston is at the beginning of its stroke. Now, assume that the circumference a b m also represents, on a small scale, the path of the center of the crank-pin ; then the diameter y x of this circle will represent the length of the stroke of the piston ; the position of this diameter is found by drawing a straight line through the point y (the center of the eccentric when the piston is at one end of its MODERN LOCOMOTITE CONSTRUCTION. 53 stroke) and the renter r. Also assume that the pointy represents the center of the crank-pin when the piston is at the beginning of its stroke. To make the construction as plain as possible, divide the diameter y x into 24 equal parts, each representing one inch of the stroke of piston, and for convenience number the divisions as shown. The arrow marked 1 shows the direction in which the valve must travel, and arrow 2 indi- cates the direction in which the center y must travel. Now it must be evident, because the points >i and C-i will always be in the same line, that during the time the center y of the eccentric travels through the arc y g, the valve not only opens the steam port, but, as the circumference a b m indicates, travels a little beyond the port, and then closes the same, or, in short, during the time the center of eccentric travels from y to //, the port has been fully opened and closed; and the moment that the center of eccen- tric readies the point g, the admission of steam into the cylinder is stopped. We have assumed that the point y also represents the position of the center of crank-pin at the beginning of the stroke ; and, since the crank and eccentric are fastened to the same shaft, it follows that during the time the center of eccentric travels from y to g the crank-pin will move through the same arc, and when the steam is cut off the crank-pin will be at the point g. Therefore, through the point g draw a straight line g k per- pendicular to the line y x ; the line g k will intersect the line y x in the point k, and this point coincides with the point mark 20 ; hence steam will be cut off when the piston has traveled I'd inches from the beginning of its stroke. The manner of finding the point k is precisely similar to that of finding the point c, in Fig. 54. The angle m y c will be the angular advance of the eccentric. LEAD WILL AFFECT THE POINT OF CUT-OFF. 72. In Fig. f>5 the valve had no lead ; if, now, in that figure, we change the angular advance m </ c of the eccentric so that the valve will have lead, as shown in Fig. 56, then the point of cut-off will also be changed. How to find the point of cut-off when the valve has lead is shown in Fig. 56. EXAMPI.K '10. The lap of valve is 1 inch, its travel 5 inches ; lead J of an inch (this large amount of lead has been chosen for the sake of clearness in the figure); stroke of piston, - J4 indies ; at what part of the stroke will the steam be cut off? On the line A 77, Fig. f>(>, lay off the exhaust and steam ports ; also on this line find the cen- ter i- of the circle <i // /// in a manner similar to that followed in the last construction, namely, by placing the valve in a central ^= position, as shown by the dotted lines and marked I), and then adopting the edge c of the valve as the center of the circle a li in; or, to use fewer words, we may say from the outside of the edge s of the steam port, lay off on the line .1 //a point < whose distance from the edge s will be equal to the lap, that is, 1 inch. From ' as a center, and with a radius of 24 inches (equal 4 of the travel), describe the circle a b m, whose circumference will represent the path of the center of eccentric. The lead of the valve in a locomotive is generally :; '.., 54 MODERN LOCOMOTIVE COXSTKUCTIOX. and sometimes as much as y- 8 - of an inch, when the valve is in full gear, in this exam- ple we have adopted a lead of J of an inch for full gear, hence, draw the section of the valve, as shown in full lines, in a position that it will occupy when the pis- ton is at the beginning of its stroke, and consequently the distance between the edge c., of the valve and the edge s of the steam port will, in this case, be J of an inch. Through r 2 draw a straight line perpendicular to A B, intersecting the circumference a b m in the point y ; this point will be the center of the eccentric when the piston is at the beginning of its stroke, and since it is assumed that the circumference a b m also represents the path of the center of the crank-pin, the point y will also be the position of the center of the crank-pin when the piston is at the commencement of its stroke. Through the points y and c draw a straight line y x, to represent the stroke of the pis- ton, and divide it into 24 equal parts. Through the point s draw a straight line per- pendicular to A B, intersecting the circumference a b m in the point </, and through <y draw a straight line perpendicular to y x, and intersecting the latter in the point k ; this point will be the point of cut-off. If now the distance between the point k and point 19 is of the space from 19 to 20, we conclude that the piston has traveled 19J inches from the beginning of its stroke when the admission of steam into the cylinder is suppressed. Here we see that when a valve has no lead, as in Fig. 55, the admission of steam into the cylinder will cease when the piston has traveled 20 inches; and when the angular advance of the eccentric is changed, as in Fig. 56, so that the valve has \ of an inch lead, the point of cut-off will be at 19J inches from the beginning of the stroke, a difference of of an inch between the point of cut-off in Fig. 55 and that in Fig. 56. But the lead in locomotive valves in full gear is only about -<fa of an inch, which will affect the point of cut-off so very little that we need not notice its effect upon the period of admission, and, therefore, lead will not be taken into consideration in the following examples. THE TRAVEL OF THE VALVE WILL AFFECT THE POINT OF CUT-OFF. 73. Fig. 57 represents the same valve and ports as shown in Fig. 55, but the travel of the valve in Fig. 57 has been increased to 5f inches. The point of cut-off k has been obtained by the same method as that employed in Figs. 55 and 56, and we find that this point k coincides with point 21. Now notice the change caused by an increase of travel ; when the travel of the valve is 5 inches, as shown in Fig. 55, the admission of steam into the cylinder will cease when the piston has trav- eled 20 inches from the commencement of its stroke, and when the travel of the same valve is increased f of an inch, as shown in Fig. 57, the admission of the steam will not be suppressed until the piston has traveled 21 inches. Here we notice a difference of 1 inch between the two points of cut-off. Bi;t it must be remembered that when the travel of a valve for a new engine is to be found or established, the point of cut-off MODEKN LOCOMOTIVE CONSTRUCTION. does not enter the question; we simply assign such a travel to the valve that steam ports will be fully opened, or give it a slightly greater travel when the valve is in full gear; and how to find this travel has been explained in Art. 59. The point of cut-off is regulated by the lap and position of the eccentric. 74. In order to find the point of cut-off it is not necessary to make a drawing of the valve, as has been done in Fig. 55. The only reason for doing so was to present the method of finding the point of cut-off to the beginner in as plain a manner as possible. In order to show how such problems can be solved without the section of a valve, and consequently with less labor, another example, similar to Example 19, is introduced. I'A\Mi'i.K 21. Lap of valve is If inches; travel, 5 inches; stroke of piston, 24 inches: width of steam port, 1 \ inches; find the point of cut-off. Fig. .~>S. Draw any straight line, as A B; anywhere on this line mark off 1J inches, equal to the width of the steam port. From the edge s of the steam port lay off on the line A B & point c, the distance between the points s and c being If inches, that is. equal to the amount of lap. From c as a center, and with a radius equal to half the travel, namely, 2if inches, draw a circle a b m; the circumference of this circle will rep- resent the path of the center of the eccentric, and also that of the (-rank-pin. Through .s draw a straight line i h perpendicular to A Ji\ this line i li will intersect the circum- feivnee H li m \\\ the points // and </. Through the points y and c draw a straight line y x; the diameter // ./ will represent the stroke of the piston. Divide y x into 24 equal parts; through the point // draw a straight line y k perpendicular to // .r, and intersect- ing // .r in the point , this point is the point of cut-off. Since k coincides with the point 18, it follows that the piston had traveled IS inches from the beginning of its stroke when the flow of the steam into the cylinder ceased. 7"). Now we may reverse the order of this construction and thus find the amount of lap required to cut off steam at a given portion of the stroke. EXAMPLE 22. Travel of valve is .Vf inches; stroke of piston, 30 inches; steam to be cut off when the piston lias traveled 22 inches from the beginning of the stroke; find the lap. Fig. 59. Draw a circle a l> in whose diameter is equal to the travel of the valve, viz., 5J inches. Through the center r draw the diameter // r. In this figure we have drawn the line // x vertically, which was done for the sake of convenience: any other position for this line will answer the purpose equally well. The circumference a h m 56 MODERN LOCOMOTIVE CONSTRUCTION. represents the path of the center of the eccentric, also that of the crank-pin ; the diame- ter y x will represent the stroke of the piston, and therefore is divided into 30 equal parts. The steam is to be cut off when the piston has traveled 22 inches from the beginning of the stroke, therefore through the point 22 draw a straight line g k perpen- dicular to y x, the line g k intersecting the circumference a b m in the point g. Join the points y and g by a straight line. Find the center s of the line y g, then, through s and perpendicular to the line y g, draw the line A B ; if the latter line is drawn accu- rately it will always pass through the center c. The distance between the points s and c will be the amount of lap required, and in this example it is 1-^ inches. Examples like the foregoing are often given in a somewhat different form. For instance, let the travel of the valve be 5f inches, stroke 30 inches, steam to be cut off at | stroke ; find the lap. Here we draw the circle a fe m and the diameter y x as before ; but instead of divid- ing the diameter x y into 30 equal parts to correspond to number of inches in the stroke, we divide it into four equal parts ; the point of cut-off k will then be at f of the diameter from its extremity y. Through the point k draw k g perpendicular to y x, and proceed as before, and thus obtain the lap required. It may also be stated that this construction will give the amount of opening of the steam poi't ; thus, in Fig. 59 the distance from s to 6 shows the amount of opening of the steam port. If, for instance, s b is equal to the width of the steam port, the latter will be opened fully; if s I is greater than the width of the steam port, the edge of the valve will travel beyond the inner edge of the gteam port ; and if s b is less than the width of the steam port, the latter will not be opened fully. This is obvious from what has been said in relation to Figs. 33, 41, 42, 43, and 44. 76. It sometimes occurs in designing a new locomotive, and often in designing stationary or marine engines, that only the width of steam port and point of cut-off is known, and the lap and travel of the valve is not known. In such cases both of these can be at once determined by the following method. EXAMPLE 23. The width of the steam port is 2 inches ; the stroke of piston, 30 inches ; steam to be cut off when the piston has traveled 24 inches from the beginning of its stroke ; find the lap and travel of the valve. Fig. 60. Draw any circle, as A B M, whose diameter is larger than what the travel of the valve is expected to be. Through the center c draw the diameter y x, and, since the stroke of the piston is 30 inches, divide y x into 30 equal parts. Steam is to be cut off when the piston has traveled 24 inches ; therefore through point 24 draw a straight line g k perpendicular to the diameter y x, intersecting the cir- cumference ABM in the point .</. Join the points y and g by a straight line ; through the center s of the line y g draw a line A B perpendicular to y g. So far, this construction is precisely similar to that shown in Fig. 59, and in order to distinguish this part of the construction from that which is to follow, we have used dotted lines ; for the remainder full lines will be used. It will also be noticed by comparing Fig. 60 with Fig. 59 that, if the diameter A B had been the correct travel of valve, then c s would have been the MOI/I-:I;\ i.ui IIMIITI (/; COXSTRUCTIOX. 57 correct amount of lap. But we commenced this construction with a travel that we knew to be too great ; hence, to find the correct travel and lap, we must proceed as follows : Join the points />' and y. From s towards li, lay off on the line A B a point b ; the distance between the points s and b must be equal to the width of the steam port plus the amount that the valve is to travel beyond the steam port, which, in this example, is assumed to be of an inch. Therefore the distance from s to b must be '2k inches. Through b draw a straight line b y. 2 parallel to B y, intersecting the line y ff in the point //._>. Through the point v/ 2 draw a straight line y. 2 #2 parallel to the line // ./, and intersecting the line A B in the point c. 2 . From c.> as a center, and with a radius equal to c 2 fc, or c 2 / 2 , describe a circle a b y.,. Then a b will be the travel of the valve, which, in this case, is 7 inches, and the distance from c 2 to s will be the lap, which, in this example, is Ij-J inches. PRACTICAL CONSTRUCTION OF THE SLIDE-VALVE. 77. It should be obvious, and therefore almost needless to remark here, that the foregoing graphical methods employed in the solutions of the problems relating to the slide-valve are applicable to every-day practice. The writer believes that these methods are the simplest and best to adopt for ordinary use, and without these it would be diffi- cult to construct a valve capable of performing the duty assigned to it. Of course, when a graphical method is employed, great accuracy in drawing the lines is necessary. We will give a practical example, in which one of the objects aimed at is to show the application of one of the foregoing methods to ordinary practice. EXAMPLE 24. The width of the steam ports is 1| inches ; length of the same, 14 inches; thickness of bridges, lj inches; width of exhaust port, 2 inches; travel of valve, 4f inches; stroke of piston, 24 inches; steam to be cut off when the piston has traveled 20f inches from the beginning of its stroke; the edges of the exhaust cavity are to cover the steam ports, and not more, when the valve stands in a central position ; construct the valve. Fig. 61. Draw a straight line A Bio represent the valve seat ; through any point in A B draw another line D C perpendicular to A B ; the line D C is to represent the center of exhaust port and the center of valve. Draw the exhaust port, bridges, and steam ports as shown. The question now arises : How long shall we make the valve? Or, in other words, what shall be the distance be- tween the outside edges of the valve < and c 2 ? If the valve had to admit steam during the whole stroke of the piston, or, as the <r * '"' Cj practical man would say, " follow full stroke," then the distance between the edges rand <-., would be equal to the sum of twice the width of one steam port pins twice the width of one bridge plus the width of the exhaust port, hence we would have 2 + 2J + 2J = 7J inches for the length of the valve. But according to the conditions given in the exam- ple, the valve must cut off steam when the piston has traveled 20? indies, therefore the valve must have lap, and the amount of lap that is necessary for this purpose must be determined by the method shown in Fig. .">!), and given in connection with Kxample 22. Following this method, we find that the required lap is \ of an inch, therefore the 58 MODERN LOCOMOTIVE CONSTRUCTION. total length of the valve will be 7i + (i x 2) = 9 inches : or we may say that the distance between the edges c and c 2 must be equal to twice the width of one steam port plus twice the width of one bridge plus the width of the exhaust port plus twice the lap, consequently we have 2+2j+2+l = 9 inches for the length of the valve. Through the points c and c 2 (each point being placed 4 inches from the center line C />), draw lines perpendicular to A B ; these lines will represent the outside surfaces containing the edges c and c 2 . These surfaces must be square with the surface A B, because, if they are not so, but are such as shown in Fig. 64, the distance between the edges c and c. 2 will decrease as the valve wears, and when this occurs the valve will not cut off the steam at the proper time. Now, in regard to the cavity of the valve. One of the con- ditions given in our example is, that the edges of the cavity must cover the steam ports, and no more, when the valve stands in a central position, therefore the inner edges i and i 2 of the valve must be 4g inches apart, which is equal to twice the width of one bridge plus the width of the exhaust port ; consequently, when the valve stands midway of its travel, the inner edges of the valve (being 4$ inches apart) and the inner edges of the steam ports coincide. Through the points i and i, (each being placed 2 inches from the center line C D), draw the straight lines i e and i. 2 c. 2 perpendicular to A B. These lines will represent the sides of the cavity containing the inner edges * and i 2 of the valve, and these sides must be square with the surface A B ; if these are otherwise, for instance such as shown in Tig. 64, the distance between the edges i and i. 2 will change as the valve wears, and then the valve will not perform its duty correctly. The depth d d 2 of the cavity is generally made from 1^ to l times the width of the exhaust port. The writer believes that making the depth of the cavity l times the 1'iy. C-t width of the exhaust port is the best practice. In our example the width of the exhaust port is 2 inches, and 2 x 1J = 3f inches, which will be the distance from d to d. 2 , that is, the depth of the cavity. The curved surface of the cavity is generally a cylindrical surface, and when it is so, as in our example, this surface must be represented in Fig. 61 by an arc of a circle. The sides i e and i 2 e. 2 must be planed, and to do this conven- iently, these sides must extend a little beyond the curved surface, towards the center C D. Consequently, through the point d. 2 draw an arc whose center is in the line C Z), and whose radius is such that will allow the sides to project about r- 6 - of an inch. Here we have lines which completely represent the cavity of the valve and the valve face. If we now add to these lines the proper thickness of metal, as shown in Fig. 62, this section of the valve will be complete. Fig. 63 shows a section of the valve taken at right angles to that shown in Fig. 62. Since the ports are 14 inches long, the cavity of the valve must be 14 inches wide, as 59 shown. Tlie amount that the valve overlaps the ends of the steam ports must be suffi- cient to prevent leakage. For a valve of the size here shown, 1 inch overlap is allowed, and tlic thickness of metal around the cavity is generally of an inch. For smaller valves the overlap at each end of the steam port is from $ to 5 of an inch, and the thickness of metal around the cavity is | of an inch. The valve here shown is suitable for a locomotive cylinder 16 inches in diameter, and a piston speed of 525 feet per minute, and the dimensions here given agree with those of the valves that are at present in use. INSIDE LAP, CLEARANCE AND INSIDE LEAD. 78. Now, a few words in regard to some other terms used in connection with the slide-valve. INSIDE LAP. The amount that the inside edges i and l z of the valve, Fig. 65, over- lap the inside edges * and s., of the steam ports, when the valve stands midway of its Fig. 66 travel, is called inside lap ; thus, the distance from s to i, or from s 2 to i.,, represents the inside lap. Its purpose is to delay the release of steam. The amount of inside lap is comparatively small, rarely exceeding & of an inch, and in many locomotives the valves have no inside lap. Rules for determining the inside lap cannot be given, because engineers do not agree on this subject. The writer believes that for slow-running locomotives, particularly if these have to run over steep grades, a little inside lap will be beneficial. For ordinary passenger locomotives running on comparatively level roads, no inside lap should be used. 7! i. INSIDE Ci.i :AKA\CE. When the valve stands midway of its travel, as shown in Fig. 66, and its inside edges i and /., do not cover the steam ports, then the amount by which each edge of the valve comes short of the inner edges of the steam ports is called inside clearance; thus, the distance fromi to s, or from 1 2 to s 2 > represents inside clear- ance. The purpose of inside clearance is to hasten the release, and is sometimes adopted in very fast-ninning locomotives. It seldom exceeds / 4 of an inch. Good judgment and great experience are required for determining the amount of clearance, and in deciding for what classes of locomotives it should be used. In ordinary pas- senger locomotives the valves have no inside clearance. SO. The widtli of opening of the steam port for the release of steam at the begin- ning of the stroke is called inside lead; thus, when the piston is at the beginning of its stroke, and the valve occupying the position as shown in Fig. 67, then the distance between the inner edges /'., of the valve and the inner edge s., of the steam port is called inside lead. The simple terms "load " and "lap" are used among engineers to desig- 60 MODERN LOCOMOTIVE COXSTJIUCT1OX. nate outside lead and lap; hence, the necessity of using the terms "inside lead" and " inside lap " when such is meant. THE EVENTS OP THE DISTRIBUTION OF STEAM. 81. In the distribution of steam during one revolution of the crank, four distinct events occur, namely : 1st. The admission of steam. 2d. The cutting off, or, in other words, the suppression of steam. 3d. The release of steam. 4th. The compression of steam. Fig. 67. The outside edges c 2 and c 3 of the valve, and the outside edges o and o 2 of the steam ports, will regulate the admission and suppression of steani ; the inner edges i and i 2 of the valve and the inner edges s and s 2 of the steam ports control the release and compression of steam. The parts of the stroke of the piston during which these events will happen can be found by the following methods : EXAMPLE 25. Travel of valve, 5 inches ; lap, 1 inch ; lead, \ of an inch ; stroke of piston, 24 inches; no inside lap or clearance. Find at what part of the stroke the admission, suppression, release, and compression will take place. In Figs. 67, 68, and 69 the valve occupies different positions, but the sections of the valve in these figures are exactly alike, because they represent one and the same valve. In Fig. 67 the distance between the edge c 2 of the valve and the edge o of the steam port is of an inch, which is the amount of lead given in our example ; hence, this position of the valve indicates that the piston is at the beginning of its stroke, and the angle m c y is the angular advance of the eccentric. In Fig. 68 the edge c. 2 of the valve and the edge o of the steam port coincide, and, since the valve is moving in the direction indicated by arrow 2, the suppression commences, or, in other words, the valve is cutting off steam when it is in the position as here shown. In Fig. 69 the inside edge i of the valve coincides with the inner edge s of the steam port, and, since the valve is moving in the direction indicated by arrow 2, the release must commence when the valve arrives in the position here shown. In Figs. 67, 68, and 69 the distances from the outside edge o of the steam port to the center c of the circle a b m are equal ; that is, the points c and o are one inch apart, which is the amount of lap. The diameters of the circles a b m are all five inches, which is the travel of the valve given in the example, and the circumference of each circle represents the path of the eccentric, and also the path of the center of the crank- pin. The point y in these figures represents the position of the center of eccentric when the piston is at the beginning of its stroke. The distance between the point y MOI>I:I;\ I.OI-OMOTI i '/: c(i\sn;rcTinN. 61 .MI id in is tli<> same in all figures, and consequently the angles formed by the lines y x and in <' are equal and represent the angular advance of the eccentric. When the valve occupies the position as represented in Fig. 67, the center line of crank will coincide with the line A Z?; and since the piston will then be at the beginning of its stroke, it follows that the line A B will indicate the direction in which the piston must move. In order to compare the relative position of the piston with that of the valve with as little labor as possible, we shall assume that the direction in which the pis- ton moves is represented by the line y x, instead of the line A Z?; hence the point y will not only show the position of the center of the eccentric, but it will also indicate the position of the cent* of the crank-pin when the piston is at the commencement of its stroke. If these remarks are thoroughly understood, there will be no difficulty in com- prehending that which is to follow. Now let us trace the motions of the valve and piston and thus determine at what part of the stroke the events (previously named) will take place. When the crank-pin is moving in the direction as indicated by the arrow marked 1, Fig. 07, the center of eccentric will move through part of the circumference, a b m, and the valve will travel in the direction indicated by the arrow 2, thus opening the steam port wider and wider until the end b of the travel is reached ; then the valve will commence to return, and as it moves toward the center c, the steam port gradually closes, until the valve reaches the position as shown in Fig. 68 ; then the steam port will be closed and steam cut off. To find the position of the piston when the valve is cutting off steam, we draw through the edge c. 2 of the valve, Fig. 68, a straight line c., y, perpendicular to A B, intersecting the circumference a b m in the point //; through this point draw a line perpendicular to y x intersecting the latter in the point k, and this point k being 19J inches from y indicates that the piston has traveled 19J inches from the beginning of its stroke before the steam is cut off, and that steam has been admitted into the cylinder during the time the piston traveled from y to k. As the piston continues to move towards the end x of the stroke, the valve will move in the direction of the arrow 2, Fig. 68, and the steam port will remain closed so that no steam can enter the cylinder or escape from it ; hence the steam that is now confined in the cylinder must push the piston ahead by its expansive force, but the moment that the valve reaches the position as shown in Fig. (i!) the release of steam will commence. To find the corresponding posi- tion of piston we draw through the edge c., of the Valve, Fig. 69, a line c.,y, perpendicular to A B, intersecting the circumference a b i in the point g. Through this point draw a line <l I; perpendicular to y x, intersecting the latter in the point k, and this point k being 22j| inches from the beginning of the stroke indicates that the piston has trav- eled through this distance when the release of steam commences. Now notice, the steam is cut off when the piston has traveled 19 inches, and the release of steam com- mences when the piston has traveled 22;' indies; consequently the steam is worked expansively during the time the piston moves ::; indies of its stroke. The steam port will remain open to the action of the exhaust during the time the piston completes its 62 MODERN LOCOMOTirE CONSTRUCTION. stroke and moves through a portion of its return stroke. In the meantime the valve will move to the end a of the travel and return as indicated by arrow 4, and the moment that the valve again reaches the position shown in Fig. 69, the release of steam will be stopped. To find the corresponding position of the piston, draw through the edge c 2 of the valve, Fig. 69, a straight line c 2 m perpendicular to A B, intersecting the circum- ference a b m in point m. Through this point draw a straight line m k., perpendicular to y x, and intersecting the latter in the point k.,. Since the distance between the points x and k. z is 22 1 inches, it follows that the piston has moved through 22f inches of its return stroke, by the time that the release of steam will cease. As the valve continues its travel in the direction of arrow 4, Fig. 69, the ste^m port will remain closed until the edge c 2 of the valve coincides with the outer edge o of the steam port, and during this time, the steam which remained in the cylinder is compressed, but as soon as the edge c 2 of the valve passes beyond the steam port edge o, the admis- sion of steam into the cylinder will commence. To find the corresponding position of the piston, draw through the outer edge o of the steam port, Fig. 67, a straight line o g perpendicular to A B, and intersecting the circumference a b m in the point g ; through this point draw a line g k perpendicular to y x, intersecting the latter in the point k, and since the distance between the points x and k is 23$ inches, we conclude that the piston has moved through 23 5 inches of its return stroke before the admission of steam will begin. Here we see that steam will be admitted into the cylinder before the return stroke of the piston is completed, and that is the object of lead, as has been stated before. Notice once more : the compression of steam will commence when the piston has traveled 22| inches of its return stroke, and will cease when the piston has traveled 23| inches of its return stroke ; hence the steam is compressed during the time that the piston travels through Ij inches. In each one of these figures the point y represents the relative position of the center of eccentric to that of the valve. The point g will always be found in the cir- cumference a b m, and in a straight line c 2 g drawn perpendicular to A B, the former passing through the outer edge c 2 of the valve. The reason why the point y should in all cases be found in the straight line c. 2 g drawn through the outside edge c 2 of the valve is this : the center c of the circle a b m has been placed on the line A B in such a position (as shown in these figures), so that the distance between the center c and the outside edge o of the steam port is equal to the lap, therefore the center g of the eccentric and the outer edge c 2 of the valve will always lie in the same straight line drawn perpendicular to A B. If the distance between center c and the outer edge o of the steam port is greater or less than the 'lap, then the center of the eccentric and outside edge of the valve will not lie in the same straight line drawn perpendicular to the line A B. Here, then, we can conceive the necessity of placing the center c of the circle a b in in the position as shown in these figures. The correctness of these remarks must be evident to the reader if the explana- tions in the previous article have been understood. Again, since we have assumed that the point g not only represents the center of the eccentric, but also the center of the crank-pin, it follows that, in order to determine how far the piston has moved from the beginning y of its stroke when the crank-pin is at //, we must draw a straight lino through the point <j perpendicular to y x, as has been done in these figures. See Art. 69. MOnKK.\ LOCOMOTIVE CONSTRUCTION. 63 From those constructions we can obtain our answer to Example 25, namely : Steam will be cut off, or, in other words, suppression will commence when the piston has traveled 19i inches from the beginning of its stroke, and steam will be admitted into the cylinder during the time that the piston travels through this distance. The steam will be released when the piston has traveled 22f inches from the beginning of its stroke, consequently the steam will be worked expansively during the time the piston travels through 3 inches. The release of steam will continue until the com- pression commences, which will occur when the piston has traveled 22$ inches of its return stroke. The compression will cease, and the admission of steam commence when the piston has traveled 23| inches of its return stroke. The same answer to our example could have been obtained with less labor by a construction as shown in Fig. 70, which is nothing else but a combination of the three preceding figures; the methods of finding the different points in Fig. 70 have not been changed, and therefore an explanation in connection with this figure is unnecessary. POWER REQUIRED TO WORK PLAIN SLIDE-VALVE, ROLLER VALVES AND BALANCED SLIDE- VALVES. 82. The great aim of engineers in constructing a slide-valve for a locomotive is to produce a valve that will require as little power as possible to work it. Consequently, y Bfyinntng of " Fig. 70 when a plain slide-valve is to be used, such as we have shown in some of the foregoing articles, the valve face is made as small as it can be made, without interfering with the duties which the valve has to perform. Again, it is of very great importance to have the mechanism inside of a steam- chest as simple as possible; therefore, on account of the great simplicity of the plain slide-valve, it is more extensively used than any other kind. Yet it has its drawbacks, besides requiring a considerable amount of .force to move it forward and backward on its seat; for instance, it is liable to cut the valve sent, wear the link, rocker, pins, and eccentrics comparatively fast, and when the valve is large, it is difficult to reverse the engine. Let us for a moment consider the amount of force that will be required to move an ordinary plain slide-valve. The resistance which must be overcome in moving any (54 MODERN LOCOMOTIVE CONSTRUCTION. slide-valve is simply the friction between the valve and its seat. This friction depends upon the pressure of the valve against the seat,* and this pressure is equal to the total steam pressure iipon the back of the valve, minus the reaction of the steam pressure in the steam and exhaust ports. This state of affairs we have endeavored to illustrate in Fig. 71, in which the arrows marked 1 indicate the pressure of the steam on the back of the valve, and the arrows marked 2 indicate the reaction of the steam pressure in the ports. To present in a plain manner the subject of finding the amount of this friction, let us take the following example: The valve is 9 inches long (see Fig. 71) and 16 inches wide ; the steam pressure in steam-chest is 120 pounds, it is required to find the amount of force necessaiy to move the valve. The total pressure on the back of the valve is found by multiplying the area of the valve face by the steam pressure, hence we have 9 x 16 = 144 inches, which is the area of the valve face, and 144 x 120 = 17,280 pounds, which is the total pressure on the back of the valve, but it is not the pressure of the valve against its seat. To obtain the latter, we must deduct from the total pressure on the back of the valve the reacting pressure in the ports. The reaction of the steam pressure in the ports can only be obtained approximately, because there are no data from which we can make the calculation. It will readily be seen that the reaction of the steam press- ure in the ports, when the valve is in full gear, is affected by, and depends upon, the size of the exhaust nozzle, the speed of engine, the lap of valve, and some other details. This pressure is also variable during the travel of the valve. For our purpose here, we will take the average. From observation the writer is led to believe that in ordi- nary locomotives the reacting pressure is equal to one-third of the pressure on the back of the valve. Grant that this is true, then the total pressure acting in the direction of the arrows 2 will be equal to J^-f = 5,760 pounds. Subtracting this quotient from the total steam pressure on the back of the valve, we obtain the pressure of the valve against its seat, hence we have 17,280 5,760 = 11,520 pounds, which is the pressure of the valve against the seat. In order that the reader may obtain a better idea of the effect of this pressure, we may say that this valve has to be moved forward and backward with a load of 11,520 pounds (nearly six tons) upon its back. The friction between two cast-iron surfaces which are straight, smooth, and lubri- cated generally ranges from n, to yj- of the pressure. In this case we will adopt the former proportion. Therefore, the friction between the valve and seat is found by dividing the pressure on the valve seat by 10, hence u f l f^ L = 1,152 pounds. This 1,152 pounds is the friction, or, we may say, the resistance which must be overcome in moving the valve, therefore a force of 1,152 pounds is required to move the valve on its seat in a direction as indicated by arrow 3, and the same amount of force is also required to move the valve in azi opposite direction. To work such a valve as quickly as must be done in a locomotive will need a great amount of power ; also, whatever power is used for this purpose is a loss, because the engine will have that amount less with which to perform useful work, that is, to haul the train. It nmst also be plain to the reader that a valve working under such a pressure is * The weight of the valve being comparatively small, it is left out of the question. M01>Ki:\ COXSTSrCTIOA'. 65 very liable to cut the valve seat, and the only way that this evil may be prevented to some extent is to use the best of metal in the cylinders, and keep the valve well oiled. We have shown that this valve requires a considerable amount of force to move it on its seat, and since this force is transmitted through the eccentrics, links, rockers, and l>ii is, it follows that these will also wear very quickly. Again, to pull the reverse lever from one notch to another, on a locomotive having cylinders about 16 inches in diame- ter, is often laborious work for an engineer, and still more so in modern engines, because these generally have larger cylinders, and consequently larger valves. From the foregoing remarks we infer that although the plain slide-valve is extremely simple, and can and must be made to distribute the steam correctly, the steam pressure on the back of this valve impairs its usefulness; and consequently there is a desire existing among engineers to procure a valve in which the evil effects of pressure on the back of the same will be removed. ROLLER VALVES. BALANCED VALVES. 83. There are in use two distinct kinds of valves which require less power to work than the plain slide-valve. One kind comprises the roller valves, and to the other kind belong the balanced valves, or, as sometimes called, the equilibrium slide-valve. Although less power is required to work the roller valve than is needed for the plain slide-valve and therefore when a roller valve is used the wear of the valve gear will be reduced this valve has never been, and is not now veiy extensively used, and, in the writer's opinion, this should not be a matter of surprise, because in the con- struction of these Fiff. 72 | Steam chest cover '^iFtff.73 Fig. valves, no at- tempt has been made to remove the steam press- ure on the back of the valve, which so impaired the usefulness of the plain slide- valve. But since the roller valve is sometimes adopted, the writer believes that a description of it will be interesting to the reader. Figs. 72, 73, and 74 represent different views of this valve, and, as will be seen, the only dif- ference between the roller valve and the plain slide-valve, is that the former is constructed in such a manner as to make room for the rollers r r r, which are interposed between the steam-chest seat and the valve. These rollers are prevented from touching each other by the small axles x x x, and around these the rollers turn. These axles, with the rollers placed upon them, are riveted to the bars t t, so that when this arrange- ment is completed, as shown in Fig. 74, a small carriage is obtained on which the valve is to work. To prevent wear of the steam-chest seat and valve as much as possible, steel plates p p, Figs. 72 and 73, are laid on the steam-chest seat, but 66 MODERN LOCOMOTirfi CONSTRUCTION. not fastened to it. Two other plates u u are attached to the valve, and between these plates the carriages are made to roll. The most important dimensions are given in the figures, and the general arrangement is also plainly shown, so that a further description is unnecessary. 84. A balanced slide-valve is represented in Figs. 75, 76, and 77. This valve is extensively used in modern locomotives, and seems to be growing in favor. In the construction of these valves the correct principle has been followed, namely, the removal of the steam pressure on the back of the valve. This is accomplished by cut- ting grooves around the back of the valve, and care must be taken to cut these grooves perfectly true ; in these, strips s s s of cast-iron are accurately fitted, so that the latter may move up and down in the grooves without any perceptible play. The strips are held up by spiral springs t 1 1, as shown. Some mechanics make these springs of hard brass wire, while others prefer to use steel wire. The diameter of the wire ranges from -^ to of an inch. The number of springs generally employed is shown in the figures. When the balanced valve is to be used the under side of the steam-chest cover must be accurately planed and scraped, because, against this surface, the strips must press and make a steam-tight joint when the valve is in the steam-chest, as shown in Fig. 78. This arrangement will prevent the steam from coming into contact with the greater portion of the back of the valve, thus reducing L ^_^_^ , g nwniKTwt^j --- ---.*, . w ..,," v.~. the pressure of the valve against the valve seat, and therefore less power will be required to work it than would be needed for a plain slide-valve, and the wear in the valve gear will also be reduced. When the valve is new, and placed in the steam-chest, as shown in Fig. 78, and all ready for use, then the strips should project not more than -^ of an inch above the top of the valve. The strips should Fia. 77 \D Section through A'.*: AVI xi -IQ-T- j r> 1, not be less than If inches deep ; 2 inches is better; in fact, these should be made as deep as they can be made without choking the exhaust cavity of the valve; and % inch is about the proper width of the strips. The manner of joining them at the corners is plainly shown in the plan of the valve, Fig. 77. For the sake of distinctness the strips have been shaded in this figure. 85. Some master mechanics object to the spiral springs, because the pockets in which these springs are placed will in time fill up with tallow, and thus prevent the springs from working freely. Therefore, in place of spiral springs for holding the strips, elliptic springs made of flat steel are used, as shown in Figs. 79 and 80, and, of VO/I/.7.-.Y ro.v.x run n<>\. 67 course, when these springs are to be used, the grooves must be cut deep enough to receive them, and the pockets, as shown in Figs. 75 and 76, left out. Yet these elliptic springs are not free from objections. Some master mechanics disapprove of them because they are too strong when new, and consequently are liable to cut tlic steam-chest cover. On the other hand, if these elliptic springs are made weaker, so that they will work satisfactorily in the beginning, they will not remain so long, and become too weak to Fig. 78 hold up the strips. The result of this disagreement, among master mechanics, is that there are about as many valves wth spiral springs in use as there are with elliptical springs. All balanced valves of this kind should have a hole /, about f of an inch in diame- ter, through the top of the valve; without this hole the valve will lift off its seat. When a locomotive is running and then steam shut off, a partial vacuum will be formed in the steam-chest, causing the valve to chatter, and thus ruin its mechanism. To pre- vent the forming of a vacuum in the steam-chest, and consequently its evil effects, a vacuum valve must be attached to the steam-chest to admit air into the latter when steam is shut off during the time the engine ts in motion. Without this vacuum valve Fly. ?!t Fig. SO no balanced slide-valve must be expected to work successfully. Indeed, it is good practice to attach a vacuum valve to all steam-chests in which a plain slide-valve is working, as this will often be the means of preventing the ashes from being drawn into the cylinder and the steam-chest. When these balanced valves are properly made by mechanics, not cheap labor, good results can certainly be looked for. We find it recorded in the annual report of the "American Railway Master Mechanics' Association," for the year 1884, that a passenger locomotive with 16" x 22" cylinders, driving wheels .">4 feet in diameter, fitted with Morse balanced valves, ran 166,000 miles without any need of facing the valve seat. Another good result obtained by using the balanced valves, is that the reverse level- can easily be handled, something to be appreciated by the engineer having charge of the engine. The balanced valve, which of late seems to be the favorite, is shown in the figures, and is called the "Richardson" balanced slide-valve. But by this remark the writer does not wisli to be understood that this is the only good balanced valve; he simply wishes to state facts as they appeal- to him. 68 MODERN LOCOMOTIVE CONSTRUCTION. ALLEN VALVE. 86. The Allen valve is shown in Fig. BOA. Its general design is the same as that of an ordinary D valve with the exception that it has a supplementary steam passage P P cast into it. In this valve, as in the ordinary D valve, the outside lap, or simply lap, is equal to a g, that is to say, it is equal to the distance by which it overlaps the outer edge y of the steam port, and this lap is in no- wise affected by the supplementary steam passage ; in fact, all the defini- tions of lap, lead, linear advance of valve, angular advance of eccentric, etc., remarks and rules given in con- nection with the plain slide- valve, are not changed when the Allen valve is used. Fig. 80c shows the valve at the end of its travel. It will here be no- ticed that the thickness a f of the metal outside of the supplementary port covers a portion of the steam port S, and therefore a somewhat wider steam port may be required than for an ordi- nary slide-valve. To find the proper width of steam port for an Allen valve under these conditions, we should proceed as follows : First, find the width of steam port required for a free ex- haust for an ordinary slide- valve, as explained in Art. 43. Now referring to Art. 59, we find that for the admission of steam we require only n, of this width of port ; conse- quently, if the thickness of the wall a /is greater than -f- of the width of the port, we must make the latter correspondingly wider. To illustrate: If we find by computation, as explained in Art. 43, that the width of the steam port for a free exhaust should be 1J = 1.25 inches, then for the ad- mission of steam we shall require an opening of 1.25 x .8 = 1 inch. If, now, the thickness of the wall a /is f inch, then we shall require for the Allen valve a steam port 1 + g = 1| inches wide. This shows us that in this particular case the width of steam port for an Ah 1 en valve should be inch greater than for a plain valve, 4L_ '* K i , " -M in i . . J 'Iff T I [J f- ill .. i U r~ s / 7 J. 18>f-|- Fig. 80 D. MODERX LOCOMOTIVE COXSTRUCTI<>\. QQ When the correct width of steam port has been found as above, and the inner edge c, of tho supplementary port is to be in line with the inner edge of the steam port when the valve is at the end of its travel, as shown in Fig. 80c, then the travel of the valve will lie c(|iial to twice the sum of the width of the steam port plus the amount that the edge r overlaps the outer edge of port. It will be noticed that this rule differs slightly from that given in Art. 59 for finding the travel of an ordinary slide-valve. The cor- rertness of this travel should be checked by drawing the valve seat with the valve at the cud of its travel, as shown in Fig. 80c. If in this position the steam port is fully or very nearly uncovered so as to give a free exhaust, the travel as previously found is correct. (lencrally, when the steam ports are correctly proportioned, the travel of an Allen valve will bo less than that of an ordinary valve. The arrangement of the valve and seat should be such that when the outer edge a (Fig. S()B) of the valve admits steam into the cylinder, then the edge b of the supple- mentary port should also admit steam into the same end of cylinder; the flow of steam under these conditions is indicated by the arrows. To attain this object, it is necessary to assign to the valve seat a correct length, which is done by making a drawing of the seat and the valve in its central position, as shown in Fig. 80x, and then making b h equal to a ff, the lap. The following advantage is claimed for this valve : In high speed locomotives with the link well hooked up, say, so as to cut off at 6 inches of the stroke, the greatest width of steam port opening with an ordinary valve is about jj of an inch only; with this contraction great difficulty is often experienced to keep up a full steam pressure from the beginning of the stroke of piston to the point of cut-off ; in fact, diagrams taken under these conditions always show a marked fall of steam pressure during this period. If, now, an Allen valve is used with supplementary ports inch wide, then, instead of having a steam port opening of | inch in width, as will be the case when the ordi- nary valve is used, we shall have a port opening of double that amount, which gives a freer admission of steam, and consequently the engine, with its links hooked up, will be capable of making better time, and in some cases do the work with less fuel. But the fact that this valve is not universally adopted seems to indicate a want of confi- dence in its advantages ; indeed, we have heard mechanics of ability express the opinion that the two currents of steam flowing into the same steam port will interfere with each other's flow, thereby losing the advantage gained by an increased port opening. Fig. 80D shows different views and details of a balanced Allen valve. It is used in an 18 x 24 inch passenger engine. TO FIND THE POINT OF CUT-OFF WHEN LENGTH OF CONNECTING-ROD IS GIVEN. 87. During one revolution of the crank the piston makes two strokes; one stroke we will call the forward stroke, and the other, the return stroke. When the length of the connecting-rod is assumed to be infinite, and the valve constructed according to the foregoing methods, linving the same amount of lap at each end, then the valve will cut off equal portions of steam in the forward and return strokes. When a connecting-rod of definite length is introduced, instead of a rod whose 70 MODERN LOCOMOTIVE CONSTRUCTION. length is assumed to be infinite, but leaving everything else unchanged, then the por- tions of steam cut off in the forward stroke will not be equal to that cut off in the return stroke. To illustrate this, let us take the following example : EXAMPLE 26. The length of the connecting-rod is 4 feet (this short length has been adopted for the sake of clearness) ; stroke of piston is 24 inches ; lap of valve, l inches ; no lead, and travel of the valve 5J inches ; find at what part of the forward stroke, and also at what part of the return stroke, steam will be cut off. In order not to complicate matters, we will assume the length of the eccentric-rod to be infinite. This problem will be divided into two parts. 1st. It will be shown at what part of the forward, and also at what part of the return stroke, steam will be cut off when the length of the con- necting-rod is as- sumed to be in- finite. 2d. It will be shown at what part of the forward, and also at what part of the return stroke, steam will be cut off when the connecting-rod is 4 feet long. Fig. 81. Draw a straight line, A B ; on this lay off the exhaust and steam ports ; draw the section of the valve so that it will overlap each steam port l inches, as shown ; drawing the valve in this position, we represent it to be in its central position. Take the edge c of the valve as a center and with a radius of 2 inches (equal to half the travel) draw the circle a b m. The circumference of this circle will represent the path of the center of the eccentric, and also that of the crank-pin (see Example 19). The direction in which the crank-pin is to move is indicated by the arrow marked 1. Since there is to be no lead, draw through the outside edge o of the steam port a straight line i h perpendicular to A J5, intersecting the circumference a b m in the point y and y. The point y will be the center of the eccentric, and also the center of the crank-pin when the piston is at the beginning of its forward stroke, and the point g will represent the center of the eccentric and that of the crank-pin at the moment that steam is cut off in the forward stroke. Through the points y and c draw the diameter y x, which will represent the stroke of the piston ; divide y x into 24 equal parts ; each part will then represent one inch of the piston's stroke. The direction in which the piston moves during the forward stroke is indicated by the arrow 2, and consequently, in the return stroke the piston must move in the direction as indicated by the arrow 3. Since y is the beginning of the forward stroke, we commence at y in marking the Min-:i;.\ i.ucoMornE m.\sn;i < TION. 71 inches '2, 4, 6, etc., on the right-hand side of x y; and because x is the beginning of tlic return stroke, we commence at ./ in marking the inches 2, 4, 6, etc., on the left-hand side of ./' /;. Through the point y draw a straight line perpendicular to y x, intersecting the latter in the point /.-, which is found to be located 18f inches from the point y, therefore tin- piston will travel 18jf inches from the beginning of its forward stroke before steam is cut off. So far, the construction is similar to that shown in Fig. 5o, and explained in Kxample l!>. We have assumed that the diameter // ./ represents the stroke of the piston, the point // the beginning of the forward stroke, aud the point x the beginning of the return stroke. But in these constructions, the center of the crank-pin and the center of eccentric are always assumed to be represented by the same point, therefore the point x will also represent the position of the center of eccentric, when the piston is at the beginning of the return stroke. Since the amount of lap is the same at either end of the valve, the center of eccentric must travel from the beginning x of the return stroke through an arc equal to the arc y <j in order to reach the position at which the steam will be cut off in this stroke ; therefore the arc x fj 2 must be made equal to the arc y y. The best way to accomplish this is to draw a line i, h 2 through #, and per- pendicular to A B, intersecting the circumference a b m in the point ff 2 , then the arc x y., will be equal to the arc y y, and the point y. 2 will be the position of the center of eccentric at which steam will be cut off in the return stroke. Through the point y., draw a straight line y 2 r perpendicular to y x, cutting the latter in the point r. The distance from x to r will represent the portion of the stroke during which steam will be admitted into the cylinder, and since, according to our con- st nu-tion, the point r is situated 18f inches from x, it follows that the piston will reach the point of cut-off when it has traveled 18 inches from the beginning of the return stroke. Here, then, we see that when the length of the connecting-rod is assumed to be infinite, steam will be admitted into the cylinder during equal portions of the two strokes, or, in other words, the distance from the beginning of the forward stroke to the point of cut-off will be equal to that in the return stroke. Now let us consider at what part of the stroke steam will be cut off when the connecting-rod is 4 feet long. If the valve is drawn full size in the construction, then the diameter y x will be 5J inches long; but we have assumed that this diameter also represents the length of the stroke of piston, which is 2 feet; therefore, when we lay off the length of the connect- ing-rod, we must adopt the diameter y x as a scale 2 feet long, consequently one-half of this diameter (which is equal to the radius of the circle a b m) will represent one foot, and the length of the connecting-rod, which is 4 feet long, will be equal to four times the radius of the circle n b ///. Prolong the line // x to any length, say, to 7), then the path of the cross-head pin will lie in the line y I), or, in other words, the center of cross-head pin will always be found somewhere in the line y D. From the point y as a center, and with a radius ei|iial to the length of the connecting-rod (equal to four times the radius of the circle a // ///). describe an arc cutting the line // /> in the point //.,; this point will represent the position of the center of the cross-head pin when the piston is at the beginning of its forward stroke. From the point ./ as a center, and with a radius equal to the length of the connecting-rod, describe an arc cutting the line // I) in the 72 MODERN LOCOMOTIVE CONSTRUCTION. point # 2 , and this point will represent the center of the cross-head pin when the piston is at the end of the forward stroke or the beginning of the return stroke. The distance between the points y z and x 2 will represent the length of stroke, and will be equal to the diameter y x. Divide the distance between y 2 and x 2 into twenty-four equal parts and number them as shown. The arrow marked 4 indicates the direction in which the piston moves during the forward stroke, and arrow 5 indicates the direc- tion of the motion of the piston during the return stroke. From the point g in the circumference a I m as a center, and with a radius equal to the length of the con- necting-rod, describe an arc cutting the line y D in the point p ; this point p will be the center of the cross-head pin, when steam is cut off in the forward stroke of the piston, and, as will be seen in the figure, the point p is situated midway between the divisions marked 17 and 18, and therefore indicates that steam will be cut off when the piston has traveled 17J inches from the beginning of the forward stroke y z . From the point fj. 2 (in the circumference a b tn) as a center, and with a radius equal to the length of the connecting-rod, describe an arc cutting the line y D in the point s ; this point s will be the position of the center of the cross-head pin when steam is cut off in the return stroke, and, as will be seen in the figure, it is situated 19f inches from the beginning of the return stroke x 2 , and therefore indicates that steam will be cut off in the return stroke when the piston has traveled 19f inches from x 2 . Here, then, we see that when the connecting-rod is 4 feet long, steam will be cut off in the forward stroke when the piston has traveled 17 inches, and in the return stroke steam will be cut off when the piston has traveled 19f inches, making a difference of 2 J inches between the two points of cut-off. This difference is caused by the an- gularity of the connecting-rod, or, in other words, by the angle formed between the center line of the connecting-rod and the line y D. This angle can be reduced by making the connecting- rod longer, but not changing the length of the stroke ; with this change the difference in position between the points of cut-off in the forward and return strokes will be- decreased. But in all engines in which the valve receives its motion direct from the eccentric, with an equal amount of lap and lead at each end of the valve, there will always be a difference in the position of the points of cut-off, even if the connecting-rod is comparatively long. Should it be desirable to make the valve in these engines to cut off equal portions of steam in the return and forward strokes, then the only way that this can be accomplished is by giving the valve more lap or lead at one end than at the other. When a link is interposed between the valve and the eccentric as shown in the locomotive valve gear, Fig. 29, then the valve can be made to cut off equal portions of steam in the forward and return strokes, without making a diffei-ence in the lap or lead of the valve. Indeed, in locomotives the amount of lap at each end of the valve is always equal, and the lead for full stroke at each end of the valve is also equal. 88. When the valve, or the valve gear, is constructed so as to make the valve cut off equal portions of steam in the forward and return strokes, the cut-off is said to be Fig.82 MODERX LOCOMOTIVE CONSTRUCTION. 73 equalized. To equalize the cut-off in a locomotive, the saddle-pin A is moved out of the center of the link, as shown in Fig. 82, that is, the center of the saddle-pin is moved a certain distance towards the center from which the link has been drawn; and besides this, the lifting-shaft arms must be made of the proper length, and the lifting shaft placed in the correct position. To determine how much the saddle-pin must be moved out of center, and what length the lifting-shaft arms should be made, and where to place the lifting shaft so that the cut-off will be equalized, we shall show later. In a locomotive it is of great importance to equalize the cut-off, as this will cause the engine to work smoother and better than with a cut-off not equalized. Again, an ei|uali/.e<l cut-off will produce an exhaust at regular and equal intervals, an attainment which is in itself of the greatest importance, because when an engine is running the sound of the exhaust indicates to the engineer the working conditions of such parts of mechanism as are out of sight; hence the engineer, besides keeping a strict look-out for the parts of mechanism which are in sight, and performing other duties imposed upon him, constantly listens to the exhaust, and as long as this beats at regular and equal intervals he knows that the valve and valve gear are in good working order, or, so to speak, are in a healthy condition ; but as soon as the exhaust commences to beat at irregular or unequal intervals, the engineer accepts this fact as a warning that some- thing is seriously wrong, and that an immediate examination of his engine is absolutely necessary. 89. In the foregoing construction we have assumed that the eccentric-rod is of an infinite length. Such an assumption will in no wise interfere with the positions of the points y and ar, which indicate the position of the center of eccentric when the piston is at the beginning of the forward and return strokes, and if these points are located with absolute exactness, according to foregoing instructions, the positions of these points will be absolutely correct. But these remarks do not apply to the points g and g. 2 , which indicate the positions of the center of eccentric at the moment that the steam is cut off in the forward and return strokes. To find the correct positions of the points g and g t , we should take into considera- tion the length of the eccentric-rod, which, on account of its angularity during the travel of the valve, will somewhat affect the positions of the points // and g. 2 , and conse- quently the points of cut-off will also be affected. Yet the change in the positions of the points f/ and //._, which will occur when the length of the eccentric-rod is taken into consideration, will be so slight, that for ordinary engines it will hardly be appreciable, and therefore may be neglected. But, in equalizing the cut-off in locomotives, the length of the eccentric-rod is taken into account, as will be seen later. CHAPTER III. VALVE GEAR. CONSTRUCTION OF LINKS. KOCKERS. 90. Figs. 83 and 84 represent a rocker such as is used in American locomotives. The general practice in locomotive construction is to make the rockers of wrought-iron, although occasionally we find them made of cast-iron. The arms and the shaft are forged in one piece. The holes in the end of the arms should be tapered, the taper being equal to J of an inch in 12 inches ; that is, in a hole 12 inches deep its diameter at one end should be of an inch larger than the diameter at the other end. Some makers adopt a greater taper, sometimes as great as 3 of an inch in 12 inches. The pins are made to fit these holes very accurately, so that they must be driven home with a hammer. The pins are made of wrought-iron, and are case-hardened. The reason for making the holes in the rocker-arms tapered, is that the pins can be driven out with greater ease, and without injuring or upsetting their ends. On the other hand, if these holes have no taper, and the pins are fitted into the rockers as firmly as is required in a locomotive, then the pins will need so much hammering in driving them into or out of the holes as to produce injurious result. The design of the locomotive generally limits the length of the rocker-shaft between the arms, but when there is room enough the length of the rocker-shaft should be at least 12 inches for large locomotives, and not less than 9 inches for smaller engines. The diameter of the shaft must be such that it will have sufficient strength to resist the severest stress to which the rocker may be subjected without springing or twisting the shaft to any appreciable extent. The greatest stress to which a rocker can be subjected will occur when an engine is to be started after it has been allowed to stand still for some time, for the following reasons : 1st. When an engine is to be started after standing still for some time, the valve seat will be dry, and it will not be lubricated until the engine has made a few turns, consequently a greater force will be required to move the valve when the engine is commencing to move than after it has been in motion for some time. 2d. Besides the force necessary to overcome the friction, an additional force will be required to overcome the adhesion caused by the oil that remained between the valve and its seat when the engine was stopped. 3d. In starting an engine the valve may occupy a position as shown in Fig. 84, that is, the valve covering both steam ports. When this happens the friction between MODERX LOCOMOTIVE COXSTRUCTION. 75 the valve and its seat will not be diminished by any reaction of steam pressure in the exhaust or steam ports ; therefore the friction between the valve and its seat will be proportional to the total steam pressure upon the back of the valve. Here, then, we see that, in starting an engine, considerably more power will be required to work the valve tluin will be necessary to work the same valve after the engine has been in motion for some time. Again, we must not neglect the force required to overcome the friction between the packing in the stuffing-box and the valve-stem, which at times may be considerable, caused by carelessly tightening the stuffing-box gland. Thus we can understand what forces a rocker has to overcome; and it must be made strong enough to do it. But to calculate the exact amount of force necessary to move a slide-valve uiiiler the foregoing conditions is impossible; we can only adopt an empirical rule, the correctness of which is based upon close observation in actual practice. The writer believes that, by making a rocker strong enough to overcome of the total strain pressure on the back of the valve, good results will be obtained. Thus, for instance : EXAMPLE 27. The length of the slide-valve is 9 inches, its breadth 16 inches, and the steam pressure in the steam-chest is 120 pounds per square inch ; what will be the greatest force that the rocker must be capable of overcoming? The total steam pressure upon the back of the valve is obtained by multiplying the area of the valve face by the steam pressure per square inch; hence we have 9" x 16" x 120 = 17,280 pounds, which is the total pressure upon the back of the valve, and J of this pressure will be the force that the rocker must be capable of over- coming without twisting or springing the shaft ; therefore -^f^ = 5,760 pounds will Fig. 86 I be the greatest stress to which the rocker can be subjected, or, in other words, the greatest force that it must overcome. Now, when we know this force we can easily determine by computation the suitable diameter of the rocker-shaft. 91. We find in books relating to the strength of material, that in the instance of a shaft which is firmly fixed at one end, having a lever attached to its other end with a force applied to the end of the lever, its diameter, which will be sufficiently large to resist twisting, is determined by multiplying the. length of the lever in inches by the force in pounds applied to the end of tlie lever, then dividing this product by a constant quantity which has been previously obtained by actual experiment, and extracting the cube root of the quotient ; the result will be the diameter of the shaft in inches. 76 MODERN LOCOMOTIVE CONSTRUCTION. This rule is used for determining the diameter of a rocker-shaft, and when we apply it we must assume the upper rocker-shaft arm 11, Figs. 83 and 84, to be the lever attached to the shaft, its length being the distance between the center of shaft and the center of pin ; the constant quantity (before alluded to) may be taken at 1,200. Hence, to find the diameter of a rocker-shaft made of wrought-iron, we have the f ollowing : RULE 14. Multiply the length of the upper rocker-arm in inches by & of the total steam pressure upon the back of the valve ; divide this product by 1,200, and the cube root of the quotient will be the diameter of the shaft in inches ; or putting this rule in the shape of a formula, we have /Length of rocker-arm in indies x ' stpilm in-cssnvc on hack of valve. Diameter of shaft = \ / - \f If the rocker-shaft is to be made of cast-iron, then the same rule is applicable, with this exception, instead of using the constant quantity 1,200, we must use the constant 1,000. EXAMPLE 28. Find the diameter of a wrought-iron rocker-shaft which has to move a slide-valve 9 inches long and 16 inches wide ; the steam pressure in the steam-chest is 120 pounds per square inch, and the length of the upper rocker-arm 10 inches. We have seen in Example 27 that of the total steam pressure on the back of the valve 9 inches long and 16 inches wide is 5,760 pounds. This 5,760 pounds is the force applied to the end of the upper rocker-arm ; therefore, according to Rule 14, we have, 10" x 5760 pounds _ 1200 and the cube root of 48 is 3.63, consequently the shaft must be 3| (nearly) inches in diameter. To find the cube root in an easy manner of any quantity, we simply refer to a table of cube roots, which will be found in any good engineer's pocket-book. 92. The length of the upper rocker-arm , Figs. 83 and 84, is limited in either direction ; that is, it must not be made too long or too short. For a slide-valve having 5 inches travel, the length of the upper arm is generally 10 inches, and for valves with less travel, the length of the upper arm can be, and should be, somewhat reduced. The reason for this is: If the length of the upper rocker-arm for a valve having 5 inches travel is made much longer than 10 inches, then the shaft will be subjected to a greater twisting stress, and consequently the diameter of the shaft must be increased, which is not always desirable. The reason why the diameter of the shaft should be made larger when the upper rocker-arm is made longer can easily be seen by examin- ing Rule 14. Again, this arm should not be made much shorter than 10 inches for a valve with 5 inches travel, on account of the custom that is followed by the majority of locomotive-builders and master-mechanics of keying the valve-rod to the valve-stem, as shown in Fig. 84, thus making a rigid connection. Now notice, in Fig. 84, that the path of the valve-rod pin is an arc, as x y, and to this arc the end of the valve-rod must accommodate itself ; and since the valve-stem must travel in a straight line, and since there is not a flexible joint between the valve rod and stem, it follows that the valve-rod must be sprung out of a straight line during the travel of the valve, and the MODERX LOCO.VOTirE COXSTRUCTIOX. 77 amount that the latter is sprung out of a straight line is equal to the line a ?>, Fig. 84. Nmv, it' tin- ui i] XT rocker-arm is made much shorter than 10 inches, leaving the tnivel'ot' tlit- valve the same as before, then the line a l> will be longer, and consequently tin- amount that the valve-rod must be sprung out of a straight line during the travel of the valve will also be greater than before, producing injurious results. The width of the rocker-arms on the line c d, passing through the center of th6 shaft, as shown in Fig. 84, is not made the same by the different locomotive-builders or master-mechanics, yet the following arbitrary rule will give a width agreeing very closely with the present practice: RULE 15. To the diameter of the rocker-shaft add one-half of the same diameter, and from this sum subtract of an inch. Or, in the shape of a formula we have : Diameter of shaft + J of diameter of shaft i of an inch = width c d of rocker-arm. EXAMPLE 29. Diameter of the rocker-shaft is 3 inches ; what must be the width of the rocker-arm at c dl 3f" + Hi" - |" = 5fV', say 5|". When the width c d of the rocker-arm is known, its thickness can be easily ascer- tained in the following manner: Assume that the arm is a lever firmly fixed atone iid and loaded at the other end, as shown in Fig. 85. Then, according to rules found in books relating to the strength of material, we find that the load which a beam or lever, firmly fixed at one end and loaded at the other, can support with safety is deter- mined by multiplying the square of the width c d by the thickness, and by a constant quantity, previously found by experiment (this quantity is generally called the " co- efficient "), and dividing this product by the length of the beam or lever. In applying this rule to the rocker we shall adopt 1,200 for the constant quantity or coefficient, and the dimensions of the rocker will be taken in inches ; therefore we have, Square of the width c d x thickness x 1200 ,, . . r- - = load. Length in inches. Now, if we know the load, the width at c d, and the length of the rocker-arm, but not its thickness, we can establish a rule from the foregoing formula which will enable us to find the thickness of the rocker-arm. RULE 16. Multiply the load in pounds by the length of the rocker-arm in inches, and divide this product by the square of the width in inches into 1,200; the quotient will be the thickness of the arm. Or, in the shape of a formula we have, Load x length in inches Square of the width c d in inches x 1200 = thickness in inches. EXAMPLE 30. What must be the thickness of the upper rocker-arm, its width c d lidng .~>i inches; length, 1(1 indies; and the valve which the rocker has to move is 9" x 16"; the steam pressure in the steam-chest is 120 pounds? The total load which a rocker has to support is equal to the greatest stress to which it can be subjected, and. as we have seen before, the latter is equal to J of the total steam pressure upon the back of the valve. 78 MODERN LOCOMOTIVE CONSTRUCTION. Now, according to Example 27, we know that of the total steam pressure upon the back of the valve 9" x 16" and with a pressure of 120 pounds per square inch is equal to 5,760 pounds, which must now be considered as the load ; consequently we have, according to Rule 16, 5760 x 10" Thickness = - - = 1.58 or 1A" inch nearly, (square of 5) x 1200 which is the thickness of the rocker-arm without the hub. 93. In a great many locomotives we find the hub h on the upper rocker-arm placed upon the outside of the latter, as shown in Fig. 86. This should be avoided as much as possible, because when the hub is so placed the arm will not only have to resist a trans- verse stress, but also an increased twisting stress, and therefore the arm and shaft must be made correspondingly strong. If the hub is placed upon the inside of the rocker- arm, as shown in Fig. 83, then the twisting stress will be reduced, but yet not alto- gether removed. To allow for this extra twist- ing stress which still remains, we have adopted in the foregoing rules a coefficient of 1,200. If the rocker-arm had no twisting stress to resist, H ' ^vt 5 FifJ.89 [ /,-,,<* ml lo',Cy.ls DJ bat simply a transverse stress, then the coefficient of 1,200 could have been increased to 1,800 ; the result of this would have been a thinner rocker-arm. On the lower rocker-arm we are generally compelled to place the hub on the outside of the arm, because room is required to clear the eccentric-rod jaw and pin, as shown in Fig. 83. Figs. 87, 88, 89, 90, and 91 show the wrought-iron rockers for the different sizes of locomotives. The diameters of the shafts and dimensions of rocker-arms have been obtained according to the foregoing rules, and are suitable for cylinders whose ports MODERX LOCOMOTIVE COXSTRVCTION. 79 are proportioned for a piston speed of 600 feet per minute, the valves having the ordi- nary amount of lap, with a steam pressure 120 pounds per square inch in the steam- chest. Comparing the dimensions given in these illustrations with the dimensions of rockers in actual use in modern locomotives, it will be seen that the former agree very closely with the latter. Of course, the length of arms given in the illustrations may have to be changed to suit some particular design of engine, and when the change is very great, then the dimensions of arms and shaft should be determined according to the foregoing rules. Again, to be very exact, we should have given a differently proportioned rocker for each size of cylinder, but this would cause a complication of patterns, which managers of private establishments and master-mechanics on railroads seek to avoid ; hence one size of rocker is generally used for two or three different sizes of cylinders that is, cylinders varying in diameter. Now, as simple as a rocker may appear to an ordinary observer, it requires care to proportion it. If the rocker is made too weak, it may still be strong enough to move the valve, yet it will spring sufficiently to derange the whole valve motion. Indeed, we have met with locomo- tives which, on leaving the round-house, had such an irregular exhaust that the engineers stopped the engines and examined the valve motions, but found that the cause of all the trouble was the springing of the rocker- shaft a trouble which would disappear after the valve face and seat became lubricated by running the engines a short distance. 94. When the valve-rod is comparatively very short, a knuckle-joint must be introduced between valve rod and stem, as illustrated in Figs. 92, 93, and 94, and which needs no further explanation. In a few cases the valve-rod end which connects to the rocker-pin is provided with brasses and a key, so as to take up the wear. But the almost universal practice in the construction of American locomotives is to drive a bush into the eye of the valve-rod, as shown in Fig. 95 (page 75). This bush is made of wrought-iron, gen- erally ^ of an inch thick for large locomotives and i of an inch for smaller en- gines. The bush is bored and turned, and then case-hardened, and finally forced into the eye of the valve-rod by an hydraulic press. Valve-rods with case-hardened bushes will need but very little repair, as the wear is comparatively slow, and when the wear of the bush becomes too great, it can be easily removed and replaced by a new one with very little expense. ftg.92 Talve rod ECCENTRICS AND STRAPS. 95. In the following illustration we have represented various eccentrics and their si nips, with all the important dimensions marked upon them. These have been selected from a number of designs adopted by some of our best locomotive builders. Figs. 80 MODERN LOCOMOTIVE CONSTRUCTION. Jflg- 147 Fly. *4S ftg, J-40 143 and 144 represent two views of an eccentric, Figs. 145 and 146 represent two views of its strap, and Fig. 147 a section of the same. Such eccentrics and straps are used on some of our large loco- motives, that is, consolidation engines having cylinders 20" in diameter and 24" stroke. Figs. 152 and 153 represent an eccen- tric, and Figs. 154, 155, 156 rep- resent the strap for the same. Eccentrics and straps of this size are used on our smallest loco- fiff. 140 motives, namely, eight-wheeled w passenger engines, with cylinders 10" in diameter and 18" stroke. When we say " smallest locomo- tives" we do not include loco- motives for mining purposes, or very light narrow-gauge loco- motives. The duty of an eccentric and its strap is to move the slide- valve forward and backward; and when, a few years ago, pumps were used in locomotive engines, then occasionally an eccentric was employed to work the pump. The action of an ec- centric, as we have stated in Art. 55, is precisely the same as that of a crank. No peculiar movement must be expected by the use of an eccentric ; the slide-valve will perform its func- tions as correctly when it re- ceives its movement from a crank as when it receives its move- ment from an eccentric ; the only reason why an eccentric is adopted is, that the use of the crank is impracticable. In Amer- ican locomotives the eccentrics and straps are generally made of cast-iron ; indeed, we may say they are always made of cast-ii'on, as we seldom find a locomotive whose eccentrics and straps are made of brass or of wrought-iron. To prevent the strap from slipping sideways off the eccentric, a recess marked (7, Flg.157 v<n>t: i;\ LocoMorirE coxsTRUcnoy. 81 Fig. 147, is turned in the strap, which fits a corresponding projection turned on the cccciitric. Some builders make the joint K L, Fig. 145, perpendicular to the center line M N of the eccentric-rod ; others make this joint not at right angles to the center line M N, as shown in Fig. 157. The advantage claimed for the latter is that the stress will be less on the nuts of the bolts which hold the two parts of the strap together. The advan- tage claimed for the former design is that no right- and left-hand pattern for the strap will be required. The oil-cup is screwed in one of the hubs J, Fig. 145 ; the reason why two hubs are cast on the strap is, as before, to avoid a right- and left-hand pattern. The eccentric-rod fits into the recess marked E E.>, Figs. 145 and 147, and is secured to the strap by three bolts. It will be noticed in Fig. 145 that the hole for one bolt is oblong ; this will allow the rod to be moved outward or inward in the recess, as may be required, and then fastened. After the correct position of the rod in the recess has been found, then the other two holes are drilled, reamed, and the bolts driven in tight, so that tin' distance from the center of the strap to the extreme end of the rod cannot be changed. Some master-mechanics object to this arrangement, and prefer to let the eccentric-rod butt against the eccentric-strap, as shown in Fig. 149. In this case, the distance between the center of the strap and the extreme end of the rod can be changed by plac- ing some thin copper strips between the strap and the rod. The eccentric is generally cast in one piece, but sometimes, for the sake of conven- ience in repairing, it is made in two parts, as shown in Figs. 148 and 151. For holding the two parts of the eccentric firmly together, some master-mechanics use studs and nuts, as shown in Fig. 148 ; others use studs with split keys or cotters, as shown in Fig. 151. The writer believes that the latter method is the best, since for the want of room in the design shown in Fig. 148 it is often extremely difficult to gain access with a wrench to the nuts. During the time of setting the valve gear the eccentrics are held in position by the set-screws, but afterwards, in the majority of locomotives, they are keyed to the axle. Of course, in a small number of locomotives, as may be inferred from the foregoing remark, the eccentrics are not keyed to the axle, and are held in position by the set screws only. The set-screws are made of steel, cupped as shown in Fig. 159, and then hardened. The key-way in the eccentric is cut before the latter is placed on the axle, but the key-way in the axle is cut after the correct position of the eccentric has been found. To cut this key- way which must be done by hand is very troublesome; hence some master-mechanics cut no key-ways in the axle, but use two keys, as shown in Fig. 160. In this case each key has teeth cut lengthways on one of its sides, as shown, so that when the keys are driven home the teeth will grip the axle. The set-screws in this case are used as an extra security against the slipping of the keys out of position. The form of the section of the strap can be made as shown in Figs. 150 and 156, or as represented in Fig. 158. By adopting the form shown in the latter figure, the strap can be made lighter, and still have the same strength as that shown in Fig. 156, but the outside diameter of the strap in Fig. 158 will necessarily be somewhat larger than that in Fiir. 15C. '.Hi. The diameter of the eccentric, and also that of the strap, should be made as 82 MODERN LOCOMOTIVE CONSTRUCTION. Fig. 142 small as possible, since by so doing not only material will be saved, but also the work expended in friction will be reduced ; and lastly, less space will be required for the eccentric to work in. This last fact is of great importance, because in a great number of locomotives the space required for the revolving of the eccentrics limits the length of the fire-box ; and since the available space for the fire-box is often barely sufficient, it follows that space should not be wasted by making the eccentrics larger than neces- sary. Thus, for instance, in eight-wheeled passenger engines the main driving-axle on which the eccentrics are fastened is placed compara- tively close to the front end of the fire-box, as shown in Fig. 142, and this distance between the main axle and the fire-box is determined by the space required for the working of the eccentrics. Now, whatever amount the radius of the eccentric is made too large, that same amount must be taken from the length of the fire-box, thus, to some extent, reduc- ing the steaming capacity of the engine. Here, then, we see the necessity of making the diameter of the eccentric and that of its strap as small as possible. The distance between the cen- ter of the main axle and that of the fire-box is generally 14 to 14 \ inches in large locomotives, and from 10 to 10J inches in the smaller locomo- tives. But here, then, the question arises, How can the correct diameter of the eccentric be determined ? In order to find the diameter of an eccentric, we must know its eccentricity ; that is, the distance between the center y of the axle and the center x of the eccentric, Fig. 142. We must also know the diame- ter of the axle on which the eccentric is fastened, and the thickness of the metal at C. When these items are known, we add together the distance between the centers x and y, half the diameter of the axle, and the thickness of the metal at (7, and multiply this sum by 2. Thus, for instance, in Fig. 143 (Art. 95) we see that the distance between the center of axle and the center of eccentric that is, the eccentricity is 2 inches, half the diameter of the axle is 3 inches, and the thick- ness of metal at C is l inches. Adding these dimensions together, we have 2^ + 3 + l = 7, and 7 x 2 = 15 inches, which is the diameter of the eccentric. From this we see that there are three items whose dimensions determine the diameter of the eccentric, namely, its eccentricity, the thickness of metal at (7, and the diam- eter of the axle. Here, then, another question arises : How can we find the dimen- sions of these three items ? The diameter of the axle is determined by rules to be explained hereafter ; hence there remain only the two former items, whose dimensions will claim our consideration. 97. In Art. 55 we have stated that the throw of an eccentric is equal to twice its eccentricity, hence the throw of the eccentric shown in Fig. 143 will be 5 inches ; we have also stated that the throw is equal to the travel of the valve for engines in which d (ft \A \ V I h & Fig. 101 xonf:n\ locoMonrE COSSTRITTION. 83 no rocker is interposed. We will now add to this statement that, when a rocker is used whose arms are of equal lengths, then the throw of an eccentric will still be equal to the travel of the valve ; on the other hand, if a rocker is used whose arms are not of equal lengths, then the throw will not be equal to the travel of the valve. Conse- quently, when the travel of the valve is given for an engine that has no rocker, or when the travel of a valve is given for an engine in which a rocker is employed whose arms are of equal length, in either case we must make the eccentricity of the eccentric equal to one- half of the travel of the valve ; we cannot make it less or more ; hence, in these two cases the shoiiest distance between the centers x and y, Fig. 142, will be equal to half the travel of the valve. When a rocker is used whose arms are not of equal lengths, then the eccentricity of the eccentric will be either more or less than half the travel of the valve. Thus for instance : EXAMPLE 31. Fig. 161. If the upper arm A of the rocker is 10 inches, and the lower arm B is 12 inches long, and the travel of the valve 5 inches, what will be the eccentricity of the eccentric ? Let the line/0 represent the position of the center of the rocker when the valve stands midway of its travel ; from the center c, and with a radius of 10 inches, describe the arc d e; on this arc lay off a point d 2 inches (one-half of the travel) from the cen- ter line/0, not measured on the arc, but on a straight line perpendicular to/0; in a similar manner lay off the point e 2% inches from/0; then the point d will represent the position of the center of the rocker-pin when the valve stands at one end of its travel, and the point e will represent the position of the center of the rocker-pin when the valve stands at the other end of its travel. From the point c as a center, and with a radius of 12 inches, describe the arc h i ; through the point d and the center c draw a straight line intersecting the arc /* i in the point * ; also through the point e and the center c draw another straight line intersecting the arc h i in the point h. The distance between the points h and i will be equal to the throw of the eccentric, and half of this distance will be the eccentricity of the eccentric. If this drawing is accurately made it will be found that the throw is 6 inches, hence, in this case, 3 inches will be the dis- tance between the centers x and y in Fig. 142, and is inch more than half the travel of the valve. EXAMPLE 32. But now suppose the upper arm A of the rocker is 12 inches long, and the length of the lower arm B, 10 inches, and the travel of the valve 5 inches as before, then what will be the eccentricity of the eccentric ? Fig. 162. From the center c, and with a radius of 12 inches, describe arc d e ; on this arc lay off as before points d and c, each point being placed 2 inches from the center line fg ; then the distance between these two points will be equal to the travel of the valve. From c as a center, and with a radius of 10 inches, describe the arc h i ; through the point d and the center c draw a straight line intersecting the arc h i in the point /, also through the point e and the center c draw a straight line intersecting the arc h i in the point Ji ; the distance between the points h and i will be equal to the throw of the eccentric, and half of this distance will be the eccentricity of the eccentric. If tliis drawing is correctly made, it will bo found that the distance between the points d and i that is, the throw of the eccentric is 4.16 inches, consequently the eccentricity 84 MODERN LOCOMOTITK CONSTRUCTION. of the eccentric will be 2.08 inches, say 2 inches, ^ of an inch less than the travel of the valve. The throw of an eccentric in the last two examples can also be found by the " simple rule of three," or, as it is sometimes called, " the simple rule of proportion." Thus, take Example 31 ; instead of finding the throw graphically as shown, we may find it thus : 10" : 12" : : 5" : throw 10)60 6 inches = the throw. Or, if we take Example 32, we have, 12": 10": : 5": throw 5 12)50 4.166 inches = throw. PROPORTIONS OF ECCENTRICS. 98. Table 12 gives the proportional dimensions of the important parts of the eccentric and strap. For instance, this table indicates that to find the thickness at C, Fig. 142, we multiply a given unit by 1, and thus obtain the dimension at C in inches. By " unit " is meant a certain number regarded as one, so that when this unit is multi- plied by the numbers as indicated, the important dimensions in inches of an eccentric and strap will have been obtained. This unit v is found in the following manner : We may assume that the friction which the eccentric has to overcome is proportional to the total steam pressure on the back of the valve, which is equal (Art. 82) to the area of the valve face multiplied by steam pressure per square inch, consequently, for finding the unit we have the following empirical rule : Multiply the square root of the total pressure on the back of the valve by the decimal .01, the product will be the unit required ; or, putting this rule in the shape of a formula, we have, .01 v'total pressure on the back of the valve. Here the decimal .01 is arbitrary, and should only be used in locomotive practice, in which it always remains the same, no matter whether the locomotive is large or small. Again, notice that the total pressure on the back of the valve depends upon the size of the valve face and the steam pressure per square inch ; and since the sizes of the valve faces vary in the different locomotives, it follows that this unit in Table 12 will also vary for the different classes of engines. EXAMPLE 33. Take, for example, a consolidation engine with cylinders 20 inches in diameter ; the average size of the valve face for these engines is 10 inches long and 20 inches wide, hence the area of the valve face is 10" x 20" = 200 square inches. Assume that the steam pressure in the steam-chest is 120 pounds per square inch, MODERN LOCOMOTIVE CONSTRUCTION. g5 we have 120 x 200 = 24,000 pounds, which is the total pressure on the back of the valve. The square root of 24,000 is 154 (here the. fraction has been neglected), and 134 x.Ol = 1.34, which is the unit required. If now we multiply this unit 1.54 by the numbers given in Table 12, we shall obtain the following dimensions of an eccentric and strap suitable to work a slide-valve with a total pressure of 24,000 pounds upon its back. Thus (see Fig. 142) : TABLE 12. A = Unit x 1 B = Unit x 2.25 C = Unit x 1 D = Unit x 1.75 E = Unit x 2.3 E 2 = Unit x .7 F = Unit x 2 The dimensions at A will be 1.54 x 1 = 1.54 inches. " " B " " 1.54 x 2.25 = 3.46 " " " " C " " 1.54 x 1 = 1.54 " " " " D " " 1.54 x 1.75 = 2.69 " " " " E " " 1.54 x 2.3 = 3.54 " " " " E., " " 1.54 x .7 = 1.07 " " " " F " " 1.54 x 2 . = 3.08 " EXAMPLE 34. Now take a small eight-wheeled passenger engine, with cylinders 10 inches in diameter. The average size of the valve face for this class of engines is 6 inches long and ll inches wide. Again, assume that the steam pressure per square inch in the steam-chest is 120 pounds. In this case we have 6" x 11.5" x 120 = 8280 pounds pressure on the back of the valve, and .01 V8280 (that is, the square root of 8280 x .01) =.91, which is the unit required. Consequently, the dimensions of an eccentric and strap suitable to work a valve with 8,280 pounds pressure upon its back will be (see Fig. 142) : The dimensions at A = .91 x 1 = .91 inches. " " " B = .91 x 2.25 = 2.04 " " " " C = .91 x 1 = .91 " " " " D = .91 x 1.75 = 1.59 " " " " E =.91 x 2.3 =2.09 " " " " E, = .91 x .7 = .63 " " " " F" = .91 x 2 = 1.82 " If we now compare the dimensions found in Example 33 with the dimensions ob- tained by measurements of eccentrics in use as shown in Figs. 143 and 145, we find these to agree very closely. The greatest difference between any two dimensions is that of the breadth of the strap at B. In our illustration the breadth is J of an inch greater than that obtained by the rule, but it must be remembered that the eccentric and strap shown in Figs. 143 and 145, although frequently used in modern locomotives, is very 86 MODERN LOCOMOTIVE CONSTRUCTION. heavy in comparison with those employed in a great many other locomotives. We also find that the dimensions found in Example 34 agree closely with those shown in Figs. 152 and 154. Here the greatest difference between any two dimensions is that of the width of the recess E for the eccentric-rod. The writer believes that if the width of the recess is made according to the rule given, namely, 2f inches instead of 2^ inches, good results will follow. Lastly, to those who are acquainted with locomotive work, it may appear that depth of the lug at F is very great when compared with the lugs on ordinary eccentric straps, but in the writer's opinion this is a great improvement, because when the holes in these lugs are reamed, the bolts turned and fitted, so that they must be driven into position, this increased depth of lug will to a great extent prevent the strap from springing out of its true circular form. LINK MOTION. 99. In Art. 61 we have seen that, when a direct connection is made between the eccentric and valve (that is, when no rocker is employed), as shown in Fig. 163, the eccentric will always travel ahead of the crank. Consequently, if, as in Fig. 163, the crank-pin occupies the position A as shown, and is to rotate in the direction as indi- cated by the arrow marked 1, then the position occupied by the eccentric will be as shown in full lines and with its center at B. If, on the other hand, the crank-pin oc- cupies the position A, as before, but is to rotate in the direction indicated by the arrow 2, then the position occupied by the eccentric must be as shown in dotted lines and MODEKX LOCOMOTIVE CONSTRUCTION. 87 with its center at C. Now if the engine is to rotate at one time in a given direction, and at another time in an opposite direction, or, in other words, if the motion of the engine is at any time to be reversed, then we must have some device by which one eccentric can be moved from its position B to (7, or we must have two eccentrics fixed on the axle for each slide-valve. The latter method, namely, the use of two eccentrics for each slide-valve, has been adopted in locomotive engines. At present, and for the sake of simplicity, we will continue the investigation of the link and its motion as used in a valve gear in which no rocker is employed. Referring now to Fig. 163, it will be readily perceived that when the engine is to turn in the direction as indicated by arrow 1, then the eccentric drawn in full lines, and whose center is at , and that alone, must move the slide-valve ; and when the engine is to rotate in the opposite direction, as indicated by the arrow 2, then the eccentric drawn in dotted lines (and not the other one) must move the slide-valve. From the foregoing we conclude that in order to reverse the engine - .4. we must disengage one eccentric and engage the other, and for this purpose the link, as shown in Figs. 164 and 165, is employed. In Fig. 164 we see that one end of each eccentric-rod is attached to the link. In this h'nk a slot or opening D D is cut lengthwise in which a block E, called the link-block, can freely but accurately move from one end to the other end of the link. The piece F is called the saddle and is bolted to the link. To the saddle the pin G is forged, and is called the link saddle-pin. The shaft H is called the lifting-shaft, or the re- versing shaft; and the arms I, J are called the lifting-shaft arms. A pin is fast- ened to the end of the lifting-shaft arm /. This pin and the link saddle-pin G work freely in a piece K, called the link hanger; this link hanger is simply a connection between the link and the lifting shaft. To the lifting-shaft arm J, one end of the reach rod is attached, as shown. The other end of the reach rod connects with the reversing lever, which is placed in the cab of the locomotive. The reversing lever is here repre- sented by its center line only ; more of this hereafter. It will readily be seen that, by moving the reverse lever in the direction as indicated by the arrow 3, the link can be raised to any position desired, and thus the motion of the engine reversed. 100. There are two methods of applying the link. First, it may be applied as shown in Fig. 164. In this case, if we move the reverse lever, we also move the h'nk and not the block, and thus set the link to any desired position. Of course, in moving the link, the end of the eceentrie-rods, which are attached to it, are carried with it. 88 MODERN LOCOMOTIVE CONSTRUCTION. Links which are moved by the reversing lever, so as to reverse the motion of the en- gine, are called " shifting links." The second method of applying the link is illustrated in Fig. 165. Here the revers- ing lever moves the valve-rod link to which the link-block is attached, but does not move the link ; or, in short, we may say that, in order to reverse the motion of the engine, the link-block is shifted in the link. In this case the link is called a " stationary link." By the term "stationary" is simply meant that the link is suspended from a stationary or fixed point ; the link itself is not stationary, because, when the engine is running, either one or the other eccentric, or both, will act upon the link, and thus keep it continually on the move. 101. It will readily be seen by referring to Fig. 164 that when a shifting link is used, and the engine is to rotate in the direction indicated by arrow 1, then the link must occupy the position as here shown ; that is, it must have been moved downwards, and for full gear the eccentric-rod pin B 2 and the center of the link-block E will lie in a horizontal line. If the engine is to rotate in an opposite direction, then the link for full gear must be lifted up until the center of eccentric-rod pin G' 2 and the center of the link-block will be in the same horizontal line. Now, referring to Fig. 165, we see that when the stationary link is used, and the engine is to rotate in the direction as indicated by arrow 1, the link-block, not the link, must be moved upwards until its center and the center of the eccentric-rod pin B. 2 lie in a horizontal line, as here shown, and when the engine is to move in an opposite direction, then the link-block must be moved downwards until its center and the center of the eccentric-rod pin C 2 are again in a horizontal line for full gear. 102. It may also be of interest to the reader to note some of the differences in the construction of the shifting and that of the stationary links. In the former the curva- ture of the link is towards the axle ; that is, the center from which the link has been drawn is located towards the axle. On the other hand, the center from which the sta- tionary link is drawn is located towards the slide-valve. Again, notice that in the shifting link the eccentric-rods are coupled to the concave side of the link, and in the stationary link the eccentric-rods are coupled to the convex side of the link. It can also be shown that when the latter link is used the lead of the slide-valve will be con- stant at whatever point of the stroke steam may be cut off, but when a shifting link is used the lead of the slide-valve will not be constant ; that is, the earlier that the steam is cut off the greater will be the lead. This we shall presently explain. We must also note the fact that when a shifting link is employed in a manner as here shown, the angular advance of the eccentric is found according to the rule given in Arts. 65, 67, but when the stationary link is used the angular advance of the eccentrics will be less. In American locomotives the shifting link is mostly used, and the stationary link is seldom found ; therefore, hereafter we will generally confine our attention to the inves- tigation of the shifting link. 103. From the foregoing the reader may be led to believe that the whole purpose of the link is to take one eccentric out of gear and place the other into gear ; and, in- deed, the writer believes that when the link was first discovered no one expected to use it for any other purpose. But soon afterwards engineers became aware of the fact that MODERX LOCOUOTirE CONSTRUCTION. gg the link could be used for cutting off steam in the cylinder at different parts of the stroke, and that on account of its simplicity it was particularly well adapted in locomo- tive engines for this purpose. Hence we may say that the purpose of the link is two- fold : first, because with it the motion of the engine can readily be reversed ; second, tlie point of cutting off steam in the cylinder can easily be changed. Thus, for instance, it' the link is placed in the position as shown in Fig. 164 it will in nowise affect the point of cutting off steam in the cylinder ; that is, if the eccentrics are set to cut off steam at J of the stroke, and the valve has the proper amount of lap, the link will not change this point of cutting off. Again, when the link is raised up so that the center of the eccentric-rod pin C 2 will be in line with the center of the link-block, then the motion of the engine will be simply reversed, and, as before, the point of cut-off will not be interfered with. If now, on the other hand, the link is raised a short distance only, so that the center of the link-block will be located, say, about midway between the end of tin' link and the link saddle F, then the travel of the valve will be shortened and the point of cutting off steam in the cylinder will be changed. DEFINITIONS. 104. Since the cylinders are placed in front of the locomotive, it follows that when the engine is traveling ahead, the crank must turn in the direction as indicated by the arrow 1, Fig. 164 ; but we have seen that when the crank rotates in this direction the eccentric B must work the valve ; therefore the eccentric B is called the forward eccen- tric, and the rod connected with it is called the forward eccentric-rod. The eccentric C is the backward eccentric, and the rod connected with it is called the backward eccentric- rod. Again, when the link occupies the position shown in Fig. 164, or when it occupies the other extreme position, that is, when the link is moved up, then the link is said to be in full gear. When the link-block stands midway between either one of its extreme positions and the center of the saddle-pin, the link is said to be in half gear ; and lastly, when the center of the link-block is in line with the center of the saddle-pin, the link is said to be in mid gear. The backward stroke of the piston is that described from the front end of the cylin- der towards the crank, and the forward stroke is that described from the back end of the cylinder towards the front. For the sake of brevity, and according to custom, we shall hereafter call the dis- tanee from the center of the eccentric to the center of the eccentric-rod pin, the length of the eccentric-rod ; or, in other words, we shall consider the eccentric and rod to be one piece, and therefore the distance from the center B to B.,, or from C to C 2 , Figs. 1(>4 and 16"), will be the length of the eccentric-rod. By the term radius of link is meant the radius of the arc I) I), drawn through the center of the opening of the link. LEAD AND ANOULAB ADVANCI. IN T CONNECTION WITH LINKS. 105. In Art. 102 we have stated that when a stationary link is employed the lead remains constant at whatever point of the stroke the steam may be cut off. The truth 90 MODERN LOCOMOTIVE CONSTRUCTION. of this will be evident by referring to Fig. 166. Here, as the position of the slide-valve indicates, the piston stands at the beginning of the forward stroke, and consequently the center of the crank-pin will be at u on the center line of motion L M. In order to enable us to trace the action of the mechanism of the valve gear as clearly as possible, we have represented the latter by its center lines. All lines drawn in full represent the position of the different parts of the valve gear when the piston is at the beginning of the forward stroke, and consequently correspond with the position u of the crank as shown. All the dotted lines represent the position of the mechanism when the piston is at the beginning of the backward stroke, and consequently will correspond with a position of the crank opposite to that of u. The line d k represents the center of the valve-rod link, and the distance from d to k represents the length of the valve-rod link from center to center of pins. The arc d I represents the link arc, that is, an arc drawn through the center of opening in the link. And here again, for the sake of simplicity, we have assumed that the center of eccentric-rod pins are located in the same arc d I. In this case such an assumption will not affect the correctness of our reasoning. The distance between the points d and / on the arc d I represents the distance between the eccentric- rod pins. The circumference of the circle / b represents the path of the center of eccen- tric. The point /in this circumference represents the position of the forward eccentric, and the point I in the same circumference represents the center of the backward eccen- tric. Both centers /and b are shown in the correct relative positions to that of the crank, when the piston is at the beginning of the forward stroke. When in this posi- tion the points /and b will lie in a line parallel to the line S T, which is drawn perpen- dicular to L M. The point f, represents the position of the forward eccentric, and b 2 represents the position of the backward eccentric when the piston is at the beginning of the backward stroke. These points/, and b. 2 will also lie in a straight line parallel to the line S T. And since the points /and b lie in the same circumference, and also in a line perpendicular to L M, it follows that the points /and b are equally distant from the center line of motion L M. The same remarks apply to the points/ and b. 2 . The full lines / d and b I represent the center lines of the eccentric-rods when the piston is at the beginning of the forward stroke, and the dotted lines b., /., and/, d 2 represent the center lines of the eccentric rods when the piston is at the beginning of the backward stroke. The link is suspended in such a manner that when the piston is at the beginning of the backward or forward stroke, the center line of motion L Mwill pass midway between the ends of the link, or, in other words, the line L M will pass midway between the points d and I. In stationary links the radius of the link arc d I is equal to the length d k of the valve-rod link. Now, since the centers /and b of the eccentrics lie in a straight line perpendicular to L M, and since the lines / d and b I are equal in length, and also, since the lines fd and b I when produced towards L would form equal angles with the line MODERX LOCOMOTIVE CONSTRUCTION. 91 /, .17, it follows that the point k from which the arc d I is drawn will also lie in the line L .17. Consequently, when the link-block is lowered, or, that is to say, when the center d of the valve-rod link is moved towards J, the point A; will remain stationary, and therefore the lead will not be changed, no matter what position the link-block may occupy in the arc d I. But when the link-block is at d, the valve motion is assumed to be in full-gear ; on the other hand, when the link-block occupies a position on the arc d I anywhere between the points d 'and /, the valve motion is not in full-gear ; hence the travel of the valve is changed, and consequently the point of cut-off is also changed without changing the lead of the valve. 106. When a shifting link is employed and no rocker used, then the linear advance of the valve and the angular advance of the eccentric, measured as explained in Art. (>7, will be equal to each other, and consequently the angular advance of each eccentric must be found as shown in Arts. 65 and 67. In Art. 102 we have stated that when a stationary link is used the angular advance of the eccentric will be less than that which is necessary when a shifting link is employed. In the first place, then, let us consider why this should be so ; and secondly, let us establish a method for finding this angular advance of the eccentrics, with sta- tionary link. We have already seen that when the piston stands at the beginning of the forward stroke, one end of the valve-rod link will be at k, Fig. 166, and when the piston is at the beginning of the backward stroke, the same end of the valve-rod link will be at n. The distance between the points k and n on the line L M must be equal to twice the linear advance of the valve. Again, since the two lines d k and d 2 n are parallel, it follows that the line d. 2 d, which is drawn parallel to L M, must be equal to the distance between the points and k, or in other words, the distance between the point d and d., must be equal to twice the linear advance of the valve. Now notice that when the piston stands at the beginning of the forward stroke the eccentric-rods / d and b I do not cross each other ; on the other hand, when the piston stands at the opposite end of the stroke the eccen- tric-rods do cross each other, as shown by the dotted lines b. 2 1 2 and /, d. 2 . Consequently the angle formed by the line/rf (when it is produced towards L) and the line L M will be less than the angle formed by the lines f, d.,, and L M, and therefore, on account of the inequality of these angles the distance between the straight line that may be drawn through the points f, b., and the straight line drawn through the points /and b will be less than the distance between the points d, 2 and d. But the angle formed between the line S Tand a straight line joining the points /and c is equal to the angular advance of the eccentric. Or again, the angle formed between the line/c and the line bz c is equal to twice the angular advance of the eccentric. But we have just seen that the distance between the points b, 2 and /is less than that between the points d. 2 and d, and consequently the angular advance of tin- eccentric will be less than the linear advance of the valve ; and lastly, since in a valve gear in which the shifting link is used, as shown in Fig. 1(>4, tin- angular advance of the eccentrics is equal to the linear advance of the valve, it follows that when a stationary link is used the angular advance of the eccentrics will be less than that which is necessary when a shifting link is em- ployed. 92 MODERN LOCOMOTIVE CONSTRUCTION. METHOD FOR FINDING THE ANGULAK ADVANCE. 107. In order to show clearly how to find the angular advance of the eccentric in a case as shown in Fig. 166, we will take the following example : EXAMPLE 35. Lap of valve is 1 inch, lead -fa of an inch, travel of valve 5 inches, length of eccentric-rods 3 feet, and the distance between the eccentric-rod pins in the link is 12 inches, throw of the eccentrics is 5 inches. Find the angular advance of the eccentrics suitable for a stationary link. Let c on the line L M, Fig. 167, be the center of the driving axle. From c as a center and with a radius equal to 2J inches (that is, half the throw of the eccentric) describe the cii-cle/k The circumference of this circle will represent "the path of the centers of the eccentrics. Draw two lines a and g parallel to the horizontal line of motion L M and each line equally distant from L M. The total distance between the lines a and g must be equal to that between the centers of the eccentric-rod pins in the link, namely 12 inches. From the center c and with a radius of 3 feet (which is equal to the length of the eccentric-rods) draw a short arc intersecting the line a in the point m. Through the point m and the center c draw a straight line m c, and prolong it to the circumference/, & 2 , on this line, fi-om the center c, and with a distance of 1-fa inches (which is equal to the linear advance of the valve), lay off the point It ; and also with the same distance (1 -fa inches) lay off from the center c on the line c m the point i. Through the points i and h draw lines perpendicular to the line c m, intersecting the circumference of the circle in the points/ and f 2 . The point /will be the center of the forward eccentric when the piston is at the beginning of the forward stroke, and the point /> will be the center of the same eccentric when the piston is at the beginning of the back- ward stroke. From the points / and /> as centers, and with a radius equal to the length of the eccentric-rod, describe small arcs intersecting the line a in the points d and d. 2 . Through the points d and /draw a straight line, then this line df will be the center line of the forward eccentric-rod when the piston is at the beginning of the forward stroke. Through d. 2 and /, draw a straight line, then this straight line d. 2 f 2 will be the center of the same eccentric-rod when the piston is at the beginning of the backward stroke. The distance between the points d and d., will be equal to twice the linear advance of the valve very nearly. We say " nearly," because this method of finding the angular advance is empirical, and can be accepted only as an approximate method. Yet in MOVER X LOCOMOTIVE COXSTRCCTIOy. 93 ordinary cast's the difference between the line d d 2 and the linear advance is inappre- ciable, and even in extreme cases, such as represented in the figure in which the eccen- tric-rods are comparatively very short, the result is very nearly correct. Yet in every case tin* distance Ix-twcen the points d. 2 and d found by the foregoing method should be compared with the linear advance of the valve, and when it is found that the dis- tance lie) ween the points d and d., is greater than twice the linear advance, the former must be corrected by changing the positions of the points/ and f 2 . The difference is generally so small that the correction necessary for the positions of the points/and/ an very readily be seen. In this example the linear advance of the valve is l/g inches, and according to the construction in Fig. 167 the angular advance of the eccentric is ! ,', of an inch measured on a line drawn through the point / perpendicular to the line S T. The point b represents the center of the backward eccentric when the piston is at the beginning of the forward stroke, and the point b. 2 represents the center of the same eccentric when the piston stands at the beginning of the backward stroke. The position of the point b is found by drawing through the point /a straight line/i, parallel to the line S T. The point b in which the line/ b intersects the circumference of the circle is the center of the backward eccentric. In a similar manner we find b 2 by drawing a line through/, parallel to S T. LEAD WITH SHIFTING LINKS. 108. In Art. 105 we have seen that the lead of the valve remains constant when a stationary link is employed. But now let us examine the state of affairs when a shifting link is used ; by so doing we will find that the lead of the valve increases when the link is moved from full-gear towards mid-gear. Fig. 168 represents a valve gear with a shifting link, and here again, for the sake of simplicity, its mechanism is represented by center lines. Also, in order to enable us to trace quickly and clearly the effect of the position of the link on the lead of the slide-valve, we have shown the latter and its seat above the line /> .17 and parallel to it. Tin- distance between the valve seat and the line /, M is immaterial ; it can be placed at any convenient height, without affecting the correctness of our reasoning; but the 94 MODERN LOCOMOTITE CONSTRUCTION. distance between the line S T and the end of the valve seat is important, and should be placed in a position as will be presently explained. In Fig. 168 the point c represents the center of the driving axle; the circumfer- ence / b represents the path of the centers of the eccentrics -/the center of the forward eccentric and & the center of the backward eccentric. The arc d I represents the link arc, that is, an arc drawn through the center of the link opening ; and the arc e g represents the arc in which the centers of the eccentric-rod pins are located. In this figure the link motion is shown to be in full-gear. The center of the crank-pin is at M, and consequently the piston will be at the beginning of its forward stroke. When the link motion is in full-gear, or in mid-gear, or in any intermediate position, the point of intersection h of the line L M with the arc d I will always represent the position of the center of the valve-rod pin; and since the distance between the valve-rod pin and the slide-valve is constant, it follows that if we know the position of the former we also know the position of the latter. If, therefore, through the point h, a straight line h i be drawn perpendicular to L M, and the valve seat placed in a position in which the distance between the line h i and the outer edge p of the port will represent the lead when the link motion is in full-gear, then we can easily determine the amount of lead when the link is set to cut off at any other portion of the stroke. Thus for instance : Let the arc d I represent the position of the link arc when the link motion is in full-gear and the piston at the beginning of the forward stroke, and also assume that the valve has i^ of an inch lead when the link motion is in this position. Draw a straight line n o any convenient distance above and parallel to L M. Through /;, the point of intersection of the line L M with the arc d I, draw a straight line h i perpendicular to L M ; the point of intersection of the line h i with the line n o will represent the edge of the valve as shown. From the line h i and on the line n o lay off a point p -fa of an inch from h i, then this point p will represent the outer edge of the steam port, and the distance between the point p and the line h i is the lead when the link motion is in full-gear. Let us now assume that the link has been moved into mid-gear as shown by the dotted lines, but without disturbing the position of the crank and that of the eccentric centers /and b. Through 7 2 , the point of intersection of the line L M with the new position of the link arc d 2 1 2 , draw a straight line k. 2 i. 2 perpendicular to L M; the distance between this line and the outer edge p of the port will represent the lead when the link is in mid- gear, and, as will be seen, this lead is greater than the lead when the link is in full-gear. 109. In a similar manner it can be shown that the lead gradually increases when the link is moved from full-gear towards mid-gear. Again, by simply increasing the length of the eccentric-rods the difference between the lead when the link is in full- gear and the lead when the link is in mid-gear is decreased. Thus, for instance, making the length of the eccentric-rods equal to twice the length as before, but not changing the position of the crank and the centers /and I of the eccentrics, the link will occupy the position as shown at x ; then by drawing the valve seat in the correct place, follow- ing the same method of construction as before, it will be seen that the difference in the lead (or in other words the distance between the line h i and h. 2 i- 2 ) when in full-gear and the lead when the link is set in mid-gear is less than when shorter eccentric-rods are used. From this we leara that the magnitude of the variable character of the lead Mf)I>Klt\ LOCOMOTIVE CONSTRUCTION. 95 depends upon the length of the eccentric-rods, and that in practice, where it is generally desirable to keep the lead as nearly constant as possible, we must make the eccentric- rods as long as the design of the engine will admit. In locomotives when in full-gear the lead is generally ^ of an inch, sometimes a little less, and this lead is increased to or of an inch, and sometimes even more, by moving the link into mid-gear. In order to avoid hereafter any misunderstanding, we again call attention to the fact that the foregoing remarks refer to link motions in which rockers are not employed. CONNECTION OP ECCENTKIC-KODS TO THE LINK. 110. It is always desirable that locomotive slide-valves should have some lead, no matter in what position the link is placed, and it certainly would be injurious if the slide-valve lapped over the steam port at the beginning of a stroke of the piston. Now to avoid having lap at the beginning of a stroke, the eccentric-rods must be correctly connected to the link. Notice, for instance, the manner in which the eccentric-rods are connected to the link in Fig. 168. There, it will be seen, the eccentric-rods do not cross each other when the piston is at the beginning of the forward stroke. But now let us examine Fig. 169, which represents precisely the same valve gear as that shown in Fig. 168, but with this difference the eccentric-rods are crossed when the piston is at the beginning of the forward stroke. Note the result. If it is the intention to use the link simply for the purpose of reversing the motion of the engine, then this manner of con- necting the eccentric-rods to the link would work very well ; but as soon as the link is used for the purpose of changing the point of cut-off, then this arrangement of eccentric- rods will have an injurious effect, particularly so in locomotive engines, as we can readily see by inspecting Fig. 169. In this figure the full lines represent the mechanism in full-gear, and the dotted lines represent the same in mid-gear. Drawing a line h i perpendicular to the line L M, and placing the valve seat in its proper position as ex- plained in connection with Fig. 168, the distance between the lino h i and the outer edge of the steam port, Fig. 169, will be the amount of lead when the link is placed in full-gear. On the other hand, when the link is placed in mid-gear, as shown by the dotted linos, and drawing a line h., i, through the point //., perpendicular to the line L 717, we find that instead of having lead as we should have the slide-valve laps over the steam port when the piston is at beginning of the stroke, which is a bad feature, and must be avoided in locomotive construction. 96 MOltKRX LOCOMOTII'K COXliTRl'CTION. PKACTICAL APPLICATION OF THE PRINCIPLES RELATING TO THE VALVE MOTION. 111. In our previous articles we have endeavored to explain the mode of pro- cedure in laying out on paper a simple valve gear, so that its mechanism can be correctly proportioned, drawn, and made in the shop. After the different parts of the valve gear are finished, they must then be correctly set in the engine. Although the methods employed in the shop for finding the position of the eccentric and other mechanism of the valve gear may appear to be different from those employed for finding the positions of the same pieces on paper, the principles on which these methods are based do not differ. In setting a simple valve gear such as is illustrated in Fig. 170, the great aim is to obtain equal leads of the slide-valve ; to obtain these we must first determine the cor- rect length of the eccentric-rod ; second, we must find the locations of the dead centers of the crank ; and lastly, the correct positions of the eccentric on the shaft. In order to show clearly the practical method employed in setting the valve gear in an engine of this kind, we will take the following example : EXAMPLE 36. The distance, as shown in Fig. 170, between the center of the crank- shaft and the line drawn midway between the steam ports of the cylinder is 8 feet 4 inches, the length of the valve-rod from center of valve to center of valve-rod pin is 20 inches, lap of an inch, lead -r 6 of an inch, and travel of the valve 5 inches. In this example it must be understood that the cylinder, shaft, and the other parts of the engine have been correctly set in line, and that all we have to do is to set the valve gear. LENGTH OF ECCENTRIC-ROD. Our first duty is to find the length of the eccentric-rod ; on paper this can be easily accomplished. Here we have only to draw the valve and rod in the center of its travel, and measure the distance from the center E of the valve-rod pin in mid position to the center of the shaft, which is equal to 100 20 = 80 inches, and this distance of 80 inches is the length of the eccentric-rod. Now if the workmanship of all the other parts of the engine is positively per- fect, so that all the dimensions of the mechanism are absolutely correct, all that we need to do is to make the eccentric-rod from the center of the eccentric-strap to the MODKKX LOCOMOTIl'K COXSTRCCTIOX. 97 editor of ihe valve-rod pin SO inches long. But such perfect workmanship is seldom procured, ami therefore the eccenti'ic-rods are generally made in two pieces, namely, the eccentric-strap and the rod proper, and constructed so that the distance between the center of strap and the center of pin E can be adjusted to suit the other parts of the machinery, and thus enabling all to work harmoniously and correctly. To obtain in an engine by measurement the distance from the center of shaft to the center I] is often a difficult matter if not impracticable, and therefore the following practical method for finding the correct length of the eccentric-rod is employed. Fasten the eccentric on the shaft in a position which will allow it to be connected to the valve-rod. In fastening the eccentric in this position, no attention need or should be paid to the position of the crank. Place and connect in position the eccen- tric-rod, which we will assume to be somewhat short. Turn the crank-shaft in a direction in which the shaft is designed to run, and when the valve arrives in the position marked 1, drawn in full lines (Fig. 171), representing it to be at one extreme end of its travel, draw along the edge a of the valve a h'ne on the valve seat; again turn the shaft in the same direction as before, and when the valve arrives in the position marked 2, shown in dotted lines, representing it to be at the other extreme end of its travel, draw along the edge b of the valve a line on the valve seat. Also on this surface draw a short line d midway between the lines a and b and parallel to the same. The distance from the line d to the line e drawn midway between the steam ports indi- cates that the length of the eccentric-rod is just that much too short and must be increased by an amount equal to this distance. If this measures i of an inch the length of rod must be increased by i of an inch. Again, if the point d had fallen on the other side of the center line e, then the distance between d and e would have indicated that the eccentric-rod is just that much too long, and must be shortened by an amount equal to this distance. In Art. 61 we find that when a valve has no lap the center of the eccentric is placed in a line perpendicular to the center line of motion, and in Art. 67 we find that when a valve has lap the angular advance of the eccentric must be laid off from this same line. Therefore in Fig. 171 the angular advance of the eccentric must be laid off from the line P drawn perpendicular to the center line of motion L M. Conse- quently, on paper, the position of the eccentric is easily found, for we have only to draw a circle whose diameter is equal to the travel of the valve, namely, 5 inches; and draw a straight line/w parallel to P and {- f an inch (which is equal to the lap and lead) away from it. The point /in which the lino/wi intersects the circle is the center of the eccentric when the crank is at L, the crank-shaft rotating in the direction as indi- cated by the arrow. But in setting the valve gear in an engine, lines like L M and P, from and on which measurements can be taken, would be a difficult matter to locate, and therefore we must seek another method, but not new principles, for laying off the angular advance of the eccentric. To do so we must find the dead centers of the crank. TO FIND THE DEAD CENTERS OF A CRANK. The dead centers A and fi of the crunk-pin, in Ki.ii. 17<, are represented by the points in which the center line of motion L M intersects the circumference of the circle 98 MODERN LOCOMOTITE CONSTRUCTION, representing the path of the center of the crank-pin. But, as stated before, we cannot locate in the engine the line L M; we must, therefore, in this case also adopt a practical method by which these dead centers can be readily and correctly found. For the sake of simplicity in our illustration we have represented a crank-disk instead of a locomo- tive wheel. This will not affect the correctness of our reasoning, for what is true in one instance will also be true in the other. On the crank-disk describe arcs I c and e d ; if the periphery of the disk is turned, then the arcs I c and e d can be described with the aid of a gauge ; if the periphery is not turned, then these arcs should be described with the aid of a scriber or sharp-pointed instrument held against the face of the disk while the shaft is revolving in its bearings ; but whichever way the arcs are described these must be true. Next turn the shaft in the direction of the arrow, until the crosshead is within a short distance from the end of the stroke, say of an inch ; while in this position mark on the slides a line g even with the end k of the crosshead. Also, while the shaft and the crosshead is in this position, place a center-punch mark j on the frame or any other fixed surface. From this point j as a center, and with a tram of any convenient length, j h, as a radius, describe a short arc intersecting the arc & c in the point c (this point c will at this instant coincide with the end h of the tram, and not as shown in the figure). Now turn the shaft in the same direction as before, causing the crosshead to complete its full stroke and part of the return stroke, and when during this motion the edge k of the crosshead touches the line g on the slide, stop turning the shaft, and while in this posi- tion describe from the point j as a center, and with the same tram as before, a short arc intersecting the arc I c in the point It. Find the point li on the arc b c, midway between the points I and c. Now turning the shaft into a position in which the ends of tram will touch the points h and j, the crank will then be on one of its dead centers, as shown. In a similar manner we can find the point i, but for this purpose we must draw another line, /, on the slide ; this time I must be drawn even with the edge n of the crosshead when it is about one-half of an inch from the beginning of the backward stroke. Then from the point j, and with the same tram-, and in the same manner as before, the points d and e are found, and the point i, midway between these points on the arc d e, is established. Turning the shaft into a position in which the points of the tram will touch the points j and , the crank will then be on the other dead center. PRACTICAL METHOD OF FINDING THE ANGULAR ADVANCE OF THE ECCENTRIC. When now the crank is placed on a dead center, the valve must then be in a position in which the steam-port opening is equal to the lead. Therefore place the crank on a dead center, say on A, and move the eccentric (which is now assumed to be connected to the valve-rod E) into a position so that the valve will have ^ of an me h lead, thereby giving the eccentric the correct angular advance. Fasten the eccentric in this position. If no inaccuracies exist in the valve gear, then by turning the crank- shaft we will find the same amount of lead when the crank is at B. If the valve has not the same lead at each end of the stroke, then inaccuracies do exist, which must be found and rectified. In setting the valve extreme accuracy is necessary ; without this failure will be the result. 112. A direct-acting valve gear, as shown in Fig. 170, is not used on locomotives. MODEKN LOCOMOTITK COXSTRUCTIOy. 99 Tliis kind of valve has been shown here to enable us to point out some fundamental principles which must be remembered in laying out any kind of valve gear. We will repeat here the most important ones in an order in which they will present themselves in laying out a valve gear for any locomotive : 1. The position of the eccentrics must be laid off from a line drawn perpendicular to the center line of motion of the valve gear, and not to the center line of crank. If the center line of motion coincides with the center line of crank, then the line drawn perpendicular to the former will also be perpendicular to the latter ; but this is merely a case of coincidence, and does not prove that the line from which the positions of the eccentrics are laid must be drawn perpendicular to the center line of crank. (See Art. 63, page 4.,.) '2. When no rocker is used the linear advance will be equal to the angular advance of the eccentric, the latter being measured on a line drawn from the center of the eccentric perpendicular to the line from which it is laid off. (See Art. 67, page 46.) 3. When no rocker is employed the eccentric will travel ahead of the crank. (See Art. 67, page 46.) 4. The use of a shifting link does not change the angular advance of the eccentric. The use of a stationary link will change the angular advance of the eccentric. (See Art. 102, page 88.) 5. When no rockers and links are employed the throw of the eccentric will be equal to the travel of the valve. (See Art. 55, page 37.) When rockers with arms of unequal lengths are used the throw of the eccentric will not be equal to travel of the valve. When the rocker-arms are of equal length the throw will be equal to the travel of the valve. (See Art. 97, page 82.) 6. The lead varies with a shifting link ; the lead is constant with a stationary link. (See Art. 102, page 88.) 7. The eccentric-rods must be connected correctly to a shifting link, otherwise there will be no lead when the link is moved towards mid-gear. (See Art. 108, page 93.) CLASSIFICATION OF LINKS. 113. When links are classified with reference to the manner of their suspension, we have, according to Art. 100, the shifting link and the stationary link. When these same links are classified with reference to their form, we have the following two classes, namely, the box link as shown in Fig. 172, and the open link as shown in Figs. 173 and 175. In American locomotives the former is seldom employed, the open link being the favorite ; and therefore we will consider the latter only. The open link can' again be divided into two classes, namely, the solid link, as shown in Fig. 173, and the built-up link, generally called the skeleton link, shown in Fig. 175. The term " skeleton link " we shall hereafter adopt for this class of links. DEFINITIONS. In all links the link arc is an arc, as a b c, drawn through the center of the opening, as shown in Fig. 173. Length of link is the length of the opening measured on a straight line joining the ends a and c of the arc a b c. 100 MODERN LOCOMOTIVE CONSTRUCTION. Radius of link is the radius with which the link arc a b c has been described, as stated in Art. 104. Eccentric-rod pin arc is an arc, as e d, drawn through the centers of the eccentric- rod pin-holes F F ; this arc is described from the same center as that used in describing the link arc a b c. !O o Fig. 172 11 'XI 1C Fig. 174 Fig. 173 Fig. 175 The manner of suspending the link and attaching the same to the rocker is plainly shown in Fig. 174. E is the lower rocker-arm ; A, the link-block pin ; 7?, the link-block ; L, the link ; S, the link-saddle ; P, the link-saddle pin ; H, the link hanger ; 6', the end of the lifting shaft arm ; and D, the lifting shaft pin. LINK-BLOCK PIN. 114. The link-block pin A (Fig. 174) is made of wrought-iron case hardened, and is fastened to the lower rocker-arm. Its end, which fits into the lower rocker-arm, should be tapered and accurately fitted into the latter. The taper should be the same as that of the valve-rod pin, as given in Art. 90. The diameter of the link-block pin at A is generally made equal to that of the valve-rod pin. Hence, the diameters of these pins will be : For 10 and 11 cylinders If diam. " 12, 13, and 14 " li " " 15 and 16 ' " If " " 17 " 18 " 13 " " 19 " 20 " li " J/0/*A7f.V LOCOMOTITE CONSTRUCTION. 101 Comparing these figures with the diameters of the pins in actual practice, it will be found that the diameters of the pins given for the smaller cylinders agree very closely with those in use, and the diameters given for 17, 18, 19, and 20 cylinders are rather large. But it must be remembered that the diameters here given have been calculated for cylinders having steam ports suitable for piston speed of 600 to 800 feet per minute, which will be required for fast passenger service, and with a steam pressure of 120 pounds in the cylinder. For freight engines in which the steam ports are often smaller than those adopted for fast passenger service, and consequently have smaller slide-valves, the diameter of these pins may be somewhat reduced, because they will have less work to do. LINK-BLOCKS. 115. The link-block is made of wrought-iron and is case hardened ; it works freely and accurately on the pin A (Fig. 174). For skeleton links the link-block is generally made in one piece ; but when the solid link is used the link-block consists of two or three pieces. Fig. 176 represents a side view; Fig. 177 an end view; and Fig. 178 a d b Fly. 177 fig. 17S L Fig. 186 a 'j. 181 a a Fig. 184 Fig. 186 section of a link-block which is made in three pieces, namely, the plates b and d, and the block c ; after the block c has been placed in the opening of the link, the plates b and d and the block c are riveted together with four g" rivets when link-block is large, and with four \" rivets when the link-block is small; the position of the rivets is shown in Fig. 176. The advantage claimed for a link-block made in this manner is, that the curved surfaces a n of the block c and the edges of the plates \> and r/ can lie finished in a slotting machine, which in some shops is more convenient to do than turning the curved surfaces of the block. Some master-mechanics prefer to make the link-block in two pieces, us shown in Figs. 17i), 180, and 181. Link-blocks made in this manner 102 MODERN LOCOMOTIVE CONSTRUCTION. consist of the plate b and the block c with the projections or flanges d d forged on to it. Close to the flanges d d small grooves e e, about -fa of an inch deep and ^ 2 - of an inch wide, are turned into the curved surfaces ; with these grooves the surfaces can be finished completely with an emery wheel, without using special tools for finishing the corners after the link-block has been case hardened. Sometimes the plate b is riveted to the block, as shown in Fig. 176, and at other times the plate I (Fig. 181) is not fastened to the block c in any manner. In this case the plate b, when the link-block is in position, must be next to rocker-arm, and is prevented from turning around by a pin f, f of an inch diameter, as shown in Figs. 179, 180 ; the block and plate being held together by the link-block pin. All link-blocks, no matter whether they are made in one piece or several pieces, are counterbored, as shown in the figures to receive the head of the link-block pin. The length of the block c is generally from one and one-quarter to one and one- half times the throw of the eccentric. This distance is measured on a straight line join- ing the ends c c of an arc drawn through the center of the block, as shown in Fig. 176. The thickness at g or k, Fig. 176, between the pin and the link is generally -fa of an inch. In a number of engines the plates b and d extend beyond the ends of the block c, as shown in Fig. 177 ; this is done to gain larger wearing surfaces. But since the extension of these plates will occasionally cause trouble in oiling the link-block, the plates are sometimes cut flush with the ends of the block, as shown in Fig. 179. The depth of the flanges at h /*, Fig. 176, is generally -fa of an inch, and we have seen them f of an inch deep ; but in the latter case the distance between the link arc and the eccentric-rod pin arc was greater than desirable. The plates b and d are generally made of an inch thick. The oil hole at i, half way through the metal, is J of an inch in diameter, and then increased to 1 or l inches in diameter, to hold the waste and oil. PROPOKilONS OF LINKS. 116. With a correctly designed shifting link motion, we obtain an equal lead when the link is in full-gear, and very nearly an equal lead when the link is in half- gear; we also obtain an equal cut-off when the link is in half -gear, and as little slip of the link on the block as possible. The slip is greater when the link is in full- gear than when it is in mid-gear, and generally the slip in forward gear will exceed the slip in the backward gear. But since there will be always more or less slip, and since this will cause wear and create " lost motion," the link must be made of such metal as will enable it to run as long a time as possible without wearing to any appreciable extent, thereby preserving the delicacy of its action. We therefore find the majority of the locomotive links made of wrought-iron, case hardened, which gives a smooth and excellent service to resist wear. During late years cast-iron links and links cast of steel have been adopted and used. These will wear faster than wrought-iron links case hardened. But the lost motion caused by wear is not undesirable, therefore cast-iron or cast-steel is mostly used for the skel- eton links. In these links very thin copper strips are inserted at (/ (/ y ,</, Figs. 184, 185, MODERN LOCOMOTIVE CONSTRUCTION. 103 so that, when the lost motion affects the correct action of the link to an extent which is hurtful to the engine, a strip or liner is taken out, and the delicate action of the link restored. Again, it' the wear of these links becomes excessive, they can be easily replaced by new links, as the cost of these is comparatively small. Figs. 185 and 186 represent the form of a skeleton link made of cast-iron, and used on a number of mogul engines having cylinders 18 inches in diameter. The same form is also adopted when the link is to be cast of steel. We have met with a few locomotives having cast-iron links of a form similar to that of a solid wrought-iron link, such as is shown in Fig. 182. But skeleton links are not always made of cast-iron or cast of steel ; often we find skeleton links made of wrought-iron case hardened, as shown in Fig. 175, and these are preferred on many railroads. In skeleton links a difficulty is experienced in putting back the end bolts after some of the liners have been taken out, because these bolt holes which incline towards each other will then not be in line ; therefore, in order to avoid this diffi- culty, some master-mechanics make the form of the links as shown in Fig. 184, in which the bolts /* h are parallel to each other. 117. The eccentric-rod pins will, in a comparatively short time, wear the holes of the link oblong ; and therefore, in order to preserve the link as long as possible, the holes e and f, Fig. 182, are bushed ; the bushing is made of wrought-iron about ^ or | of an inch thick, case hardened, and then forced into the link, usually with a hydraulic pressure of four tons. This bushing is used in wrought-iron, and also in cast links. When the wear of the pin and bushing becomes so great as to affect the action of the link, the pin and bushing can be easily and cheaply replaced by new ones. Sometimes we find links in which the bushing has been fitted loosely in the holes ; in these cases the bushing is slightly longer than the width of the link, and held fast in the eccentric- rod jaw by tightening the nut of the eccentric-rod pin, allowing the bushing to move freely in the link. Loose bushing is better adapted for cast links than for wrought- irou case-hardened links, because the former can be more readily and in less time rebored, or replaced by a new link if necessary, and with less expense than the latter. 118. The eccentric-rod pins are also case hardened. The cross-sectional area of one of these pins should not be less than half the area of the rocker-pins given in Art. 114 ; locomotive builders generally make the area of an eccentric-rod pin a little larger than half the area of rocker-pin, so as to obtain a larger bearing surface. The diameter of the eccentric-rod pins for engines having cylinders 19 or 20 inches in diameter is usually 1J inches; for engines having cylinders 16, 17, or 18 inches in diameter, l; and for smaller engines, 1 inch. 119. For locomotives having cylinders 10 inches in diameter and upwards, the distance between the centers of the eccentric-rod pins e undf, Fig. 182, generally varies from 9 to 10 inches ; and for locomotives having cylinders 16 inches in diameter and upwards, the distance between these eccentric-rod pin centers generally varies from 11 to 12 inches; sometimes, but rarely, this distance is 13 inches. The distances between the eccentric-rod pin centers shoiild not be made less than those here given, because if we do so the slip of the link on the block will lie increased. Neither can these dis- tances be made much longer, because generally the room under the locomotive will not admit longer links. 104 MODERN LOCOMOTIVE CONSTRUCTION. 120. In locomotives having cylinders 10 inches in diameter and upwards, the throw of the eccentric is from 3 to 4 inches ; and in locomotives having cylinders 16 inches in diameter and upwards, the throw of the eccentric is from 4.J to 5 inches, oftener 5 inches. Now, comparing the throw of the eccentrics with the distances between the eccentric-rod pin centers, we find that this distance varies from 2% to 2 times the throw of the eccentric. Hence, in designing a locomotive link we may make the dis- tance between the eccentric-rod pin centers equal to 2J or 2j times the throw of the eccentric. Although this is an empirical rule, it is a good rule to adopt, provided it does not make the link too long. 121. The distance between the eccentric-rod pin arc and the link arc must not be greater than necessary; it should be such as will allow -fa of an inch clear- ance between the flanges of the link-block and the ends of the eccentric-rods. By increasing this distance we also increase the slip, which must be avoided. In ordinary loco- motive practice this distance varies from 2J to 3 inches, and occasionally reaches 3 inches. 122. The length of the link, that is, the distance from c to d, Fig. 182, should be sufficiently great to allow the center of the link-block to be placed in line with the center of either one of the eccentric-rod pins, leaving a clearance sufficient for the slip, so that when running in this gear the link-block will be pre- vented from coming in contact of an inch for the least amount clear- Fly. 183 Fig. 182 with the end of the link opening. In fact, ance between the link-block and end of link opening is preferable. Consequently, to determine the length of a link, we must know the distance between eccentric-rod pins, the length of the link-block, the maximum slip, and the desired amount of clearances. The sum of these items will be the length of the link. EXAMPLE 37. The distance between the eccentric-rod pins is 12 inches ; the length of the link-block is G inches ; the maximum slip is 1 inches ; and the desired clearance at either end must not be less than J of an inch. 12" + 6" + Ijf" + 4" + 4" = 19&" = length of link. The length of links in the different locomotives having cylinders 16 inches in diameter and upwards varies from 18 inches to 19 J inches, rarely exceeding the latter dimension. 123. The radius of links in nearly all locomotives is equal to the distance between the center of the main driving axle and the center of link-block pin (sometimes called the lower rocker-arm pin) when the latter stands ill the center of its travel. MODEKX LOCOMOTIVE CONSTHUCTION. 105 [t has been found that, with this radius, the variation of the lead is sensibly equal for the front and bark strokes of the piston. Sometimes, when greater accuracy in the equalization of the lead is required, this radius of the link is made a little shorter. 1:24. In order to obtain the breadth B, Fig. 183, and the thickness T, Fig. 182, of a wrought-iron link, we should know the pressure of the valve against its seat ; but since the existing data is not sufficient to determine this pressure accurately, we will assume that the friction of the valve on its seat and which the link has to overcome in moving the valve is proportional to the total steam pressure on the back of the valve.* Consequently, for the purpose of obtaining these dimensions of the link we will adopt tlif same rule as that used for finding the principal dimensions of an eccentric, given in Art. 98. Therefore, for finding the breadth B and thickness T of a wrought-iron link we use the same units found in Art. 98, and multiply the unit by the numbers given in the following table : TABLE 13. Breadth B of wrought-iron link = unit x 1.62 Thickness T " " " = unit x .81 EXAMPLE 38. Find the breadth B and the thickness T of a wrought-iron link suit- able for a consolidation engine having cylinders 20 inches in diameter ; the length of valve is 10 inches ; breadth of the same 20 inches ; and pressure of the steam in the steam-chest 120 pounds per square inch. We find in Art. 98 that the unit for this size of slide-valve is 1.54, hence : 1.54 x 1.62 = 2.49" = breadth of link. 1.54 x .81 = 1.24" = thickness T. EXAMPLE 39. Find the breadth B and the thickness T of & wrought-iron link suitable for an eight-wheeled passenger locomotive having cylinders 10 inches in diam- eter ; slide-valve being 6 inches long and llj inches wide ; steam pressure in steam- chest 120 pounds per square inch. We find in Art. 98 that the unit for this size of slide-valve is .91, hence : .91 x l.(52 = 1.47" = breadth of link. .91 x .81 = .73" = thickness T. Now, comparing the dimensions obtained in Example 38 with the dimensions of the link in Figs. 182 and 183, which is a drawing of a link used in a consolidation engine with cylinder 20 inches in diameter, lately built and now in active service, we find that these dimensions agree very closely. It will also be found that the dimensions of other wrought-iron links obtained by this rule, suitable for locomotives having cylinders 13 inches in diameter, and others having cylinders of larger diameter, up to 20 indies, will agree very closely with the dimensions of the links in locomotives of the foregoing sixes at present in active service. * It should be understood that tin- total steam pressure on the back of the valve is greater than the pressure of the valve agaiust its Beat (see Art. 82). 106 MODERN LOCOMOTIVE CONSTRUCTION. But the dimensions of links for smaller locomotives obtained by our rule are less than the dimensions of links made according to the present practice of locomotive builders. Take, for instance, Example 39. In this we find that the breadth of the link suit- able for locomotives having cylinders 10 inches in diameter is 1.47 inches, say 1 \ inches, whereas the breadth of links in locomotives of this size, and at present in active service, is If and sometimes 2 inches. But when it is necessary to build a very light locomotive, the writer believes that links proportioned by this rule will give good satisfaction, although they will wear somewhat faster than those having a greater width. 125. The tendency in modern locomotive construction is to make the saddle-pin longer than formerly. This, in the writer's opinion, is a great improvement. The saddle-pin for locomotives having cylinders 17 up to 20 inches in diameter is now generally 6 inches long, as shown in Fig. 183. For smaller locomotives the length of saddle-pin is decreased; a saddle-pin 4 inches long will work very sat- isfactorily in locomotives with cylinders 10 inches in diam- eter. These saddle-pins should not be made shorter, unless compelled to do so by the narrow gauge of the road. The diameter of the saddle-pin is usually about one-eighth of an inch less than the diameter of the link-block pin. Figs. 187 and 188 represent a link hanger. The dimensions given are suitable for locomotives having cylinders 19 inches and others having cylinders 20 inches in diameter. Usually the holes are bushed with wrought-iron ferrules case hardened. Fig. 187 LIFTING SHAFT. 126. Fig. 189 represents an end view and Fig. 190 a plan of the " lifting shaft," or sometimes called the " reverse shaft." Two arms B B one for each link are forged to the shaft D ; the holes for the lifting-shaft pins A A in the end of these arms are tapered; the taper should be the same as that of the valve-rod pin (see Art. 90). The case-hardened lifting-shaft pins A A are made to fit these holes very accu- rately. On these pins the link hangers vibrate. The arm E is generally forged to the shaft D ; occasionally it is keyed to the shaft. The hole at C for the reach-rod pin is bushed with a wrought-iron ferrule, case hardened, usually from to YS of an inch thick. The reach-rod pin, which connects the reach-rod to the arm E, is straight and case hardened. The other end of the reach-rod is connected to the reversing lever at (7, as shown in Fig. 192. The line L B (Fig. 192) represents the center line of the reverse lever when it stands in full-gear forward, and the line A B represents the center line of the reverse lever when it stands in full-gear backward ; and when the reverse lever stands in center of the arc as shown, the link motion is said to be in mid-gear. Now when the reverse lever (which is connected by the reach-rod to the lifting shaft) is moved from A to L the motion of the engine will be reversed ; or if MODEKX LOCOMOTIVE CONSTRUCTION. 107 Reach Hod --/ax X. Fig. 189 the reverse lever is moved to any intermediate position, the travel of the valve will ! reduced, and steam in the cylinder will be cut off sooner. The diameter of the lifting shaft (Figs. 189 and 190) and the size of its arms must be sufficiently large to prevent the shaft and arms from springing. The dimensions given in the figures are those of lifting shafts generally used in locomotives which have cylinders 20 inches in diameter. For smaller locomotives, which have cylinders 10 inches in diameter, the lifting-shaft arms B B measured close to the shaft are usually 2 inches wide and f of an inch thick ; the arm E is 2 inches wide and of an inch thick ; and the shaft 2 inches in diameter. These dimensions are gradually enlarged as the diameter of the cylinder is increased. The location of the lifting shaft and the length of its arms B B will influence the equal- ization of the cut-off ; therefore it is very im- portant to assign the correct position to the lifting shaft and make the arms B B of the proper length. How to find the position of the lifting shaft and the correct length of the arms B B will be explained later. The length of the arm E is generally limited by the design of the locomotive; that is, the length of this arm must be such as will prevent the reach- rod from coming in contact with other parts of the engine. The center lines of the arms B B, and that of the arm E, do not often stand at right an- gles to each other as shown ; they should have the following relative positions: The center line A F of the arm E should stand perpen- dicular to the reach-rod when the link motion is in mid-gear ; and the center lines of the arms B B should then stand in the center of their total vibration. This will allow the end of the arm E to pass through equal arcs on each side of the line A F during the time the links are moved from full-gear forward to full-gear backward. The short arm F is usually forged to the shaft I)\ occasionally it is bolted to the shaft. To this arm F a spring counter- balance is attached which acts against the weight of links, hangers, etc., relieving the engineer of considerable hard work in reversing the engine, and enabling him to move the reverse lever as easily in one direction as in the other. Sometimes, for the purpose of counterbalancing the weight of the links, hangers, etc., volute springs are used, as shown in Fig. 191, but the writer believes that a half elliptic spring, as shown in Figs. 189 and 190, will give better satisfaction. 108 MODERN LOCOMOTIVE CONSTRUCTION. 127. Volute springs, as shown in Fig. 191, are made of steel 3 inches wide, ^ of an inch thick, the springs are 6 to 6 inches long for large locomotives. For small loco- motives these springs are made of steel 3 inches wide, J of an inch thick, and the same length as that of the larger ones. The cast-iron casing around these springs is generally bolted to the yoke brace. Elliptic springs are usually made nearly as long as the space between the frames will allow. For large engines, 4' 8" gauge, the length of these springs is usually 40 inches before compres- sion, and having 5 or G leaves of steel 2 inches wide and -fg thick. When these half ellip- tic springs are used, the rod G (Fig. 189) should be attached to the arm F in a manner as shown, which will allow the spring to be tightened or loosened without disconnecting the rod G from the spring. Reach-rods for large locomotives are usually made of 2|" x f" iron; and for smaller locomo- tives 2" x f " iron. REVERSE LEVER. 128. The design of an engine and the position of its driving wheels deter- mines the location of the reverse lever. Generally, in engines having a foot- plate the lower end of the lever can be attached to the same ; in consolidation engines or hard-coal burn- ers we are generally com- pelled to attach the lever to the frame. In all cases the reverse lever is located on the right-hand side of the engine. The reverse lever is usually made of wrought-iron ; but when the part of the lever below the arc D, Fig. 193, is very crooked which often occurs then in order to save labor in forging, the lower part is sometimes made of cast-iron and bolted to the upper part, which is made of wrought-h'on. The form of the lower end of the reverse lever is determined also by MODERN LOCOMOTIVE CONSTRUCTION. 109 the design of the engine. In consolidation engines it often happens that the reverse lever has to move between one of the rear driving wheels and the boiler, and there- fore its lower part has to be made comparatively thin and very wide, as shown in Fig. 192. In engines which have the reverse lever attached to the foot-board, the lower cin I of the lever is shaped as shown in Fig. 193, and its thickness is the same through- out ; usually 5 of an inch for large engines, and of an inch for smaller ones. The total length of the reverse lever and the location of the reach-rod pin in the same must be such as will allow the top of the reverse-lever handle 0, Fig. 192, to move through a distance of about 4 feet in large engines; and through a distance of about 3 feet 6 inches in smaller engines during the time that the link is moved from full-gear forward to full-gear backward. Now, since the distance through which the link is moved is equal to the distance between the centers of eccentric-rod pins, and since these are placed from 11 to 12 inches apart in large engines, and from 9 to 10 inches in small engines (Art. 119), we may say that the distance through which the reverse-lever handle moves should be about four times the distance through -which the link moves. The diameter of the reverse-lever pin 7?, Fig. 192, is usually 1 inch for small locomotives and li inches for large ones. These pins are case hardened. The hole C for the reach-rod pin in the reverse lever is sometimes bushed with a case-hardened bushing. 129. The arcs D are usually made of steel, fastened to the boiler, or to the foot- plate and running board. In a number of engines two arcs are employed, one on each side of the lever, as shown in Fig. 192. In other locomotives one arc only is used, which passes through an opening in the reverse lever as shown in Fig. 194. When a single arc is used it is made comparatively wide, as will be seen by comparing Fig. 192 with Fig. 194. Whether to use two arcs or the single arc is a matter of choice and judgment. The arcs should be placed as high as the design of engine will permit ; by so doing more notches, F F (Fig. 192), can be cut in the arcs, with sufficient metal for strength between them, than can be cut in arcs placed lower down. The notches F F receive the latch G. This latch is connected to the latch-handle // by the links 7, so that, when the latch-handle is pressed towards the handle of the reverse lever, the latch (i will be lifted out of the notch, and when the pressure on the latch-handle ceases, the spring K presses the latch into the notch. With this arrangement the lever can be placed and held in any desired position. The writer believes that it will give better satisfaction by placing the latch G (which slides in the clamp M) in front of the re- verse lever, as shown in Fig. 192, and not in the rear of the reverse lever, as shown in Fig. 193. By adopting the former method the reverse lever will press against the latch; but by placing the latch in the rear of the lever, the tendency will be to pull the reverse lever away from the latch, which will in a short time cause the lever to rattle and interfere with the correct action of the link motion. 130. Master-mechanics differ in opinion in regard to the number and the position Fig. 1U4 UNIVERSITY OF CALIFORNIA DEPARTMENT OF CIVIL ENGINEERING 110 MODERN LOCOMOTIVE CONSTRUCTION. of the notches in the arcs. First : A number of master-mechanics prefer the notches arranged in a manner which will hold the reverse lever in positions that cause the steam to be cut off in the cylinder at some full number of inches of the stroke. Con- sequently, we find arcs with notches cut in such positions as will cause the steam to be cut off at 6, 9, 12, 15, 18, and 21 inches of the stroke ; or at 6, 8, 10, 12, 15, 18, and 21 inches of the stroke. Besides these notches one notch is cut in the arcs to hold the link in mid-gear. With this arrangement of notches a difficulty arises, namely, it is often found that when a particular notch say the 6-iuch notch holds the reverse lever, the cylinders do not receive a sufficient amount of steam to haul the train, and when the reverse lever is moved to the next notch the 9-inch notch the cylinders receive too much steam, and therefore the steam has to be throttled, causing the locomotive to work under disadvantages. To overcome this dif- ficulty, May's Reverse Lever Latch has been invented, by which a finer gradation is ob- tained without changing the notches. This latch is shown in Figs. 195 and 196, and, as will be seen, is a very simple device. The only difference between this and the ordinary latch is, that the former is a double latch instead of a single one ; consequently, it can easily be applied to the re- verse levers at present in use without any change in the levers or arcs. Now, since a finer gradation is not a matter of convenience, but it is a saving of fuel, the advantages of May's latch, or some equally good device, will easily be perceived. But while some master-mechanics will insist on having the notches cut in the fore- going manner, others believe that whether steam is cut off at full inches, or a fractional number of inches of the stroke, is of no consequence ; hence these master-mechanics will cut as many notches in the arc as there is room for, and as close together as the strength of metal will allow. Fig. 193 shows an arc with notches cut in this manner. The distance between the centers of these notches is half an inch; sometimes the notches are cut closer than this. With notches cut in this manner a very fine grada- tion of cut-off is obtained, and fuel saved. 310DEKX LOCOMOTIVE CONSTRUCTION. Ill VALVE GEARS WITH ROCKERS. 131. Heretofore we have shown, theoretically and practically, how to set the (reentries in simple valve gears in which rockers are not employed, and in which the connections between the eccentric and valve are direct, and also in which the center line of motion of the valve gear coincided with that of the piston. Let us now continue the subject of setting the eccentrics, in the following order: First, how to find the position of an eccentric in a valve gear in which a rocker with arms of equal length is used, and in which the center line of motion of the valve gear coincides with the center line of motion of the piston. Second, how to find the position of the eccentric in a valve gear in which a rocker whose arms are not of equal length is used, and in which the center line of motion of the valve gear coincides with that of the piston. Third, to find the position of an eccentric in a valve gear in which a rocker is used, and in which the center line of motion of the valve gear does not coincide with that of the piston. TO FIND THE POSITION OF AN ECCENTRIC IN A VALVE GEAR HAVING A ROCKER WHOSE ARMS ARE OF EQUAL LENGTH, AND THE CENTER LINE OF MOTION OF THE VALVE GEAR COINCIDING WITH THAT OF THE PISTON. In order to make this subject as plain as possible, let us take the fol- lowing example : EXAMPLE 39a. Lap of valve, ii of an inch; lead, Vs of an inch; travel of valve, 5 inches ; length of each rocker- arm, 10 inches ; find the posi- tion of the eccentric. In Art. 67 we have explained how to find the position of an eccentric in a simple valve gear in which no rocker is employed, and in Art. 61 we have pointed to the fact that hi simple valve gears of this kind the eccentric must travel ahead of the crank. It is now to be shown that, when a rocker is interposed between the eccentric and valve without making any other changes in a simple valve gear, the eccentric must 1'ollow the crank, instead of traveling ahead of the same; and it is also to be shown Fig. 195 Fig. 196 112 MODERN LOCOMOTIVE CONSTRUCTION. that, when the rocker whose arms are equal in length is used, the angular advance of the eccentric will be laid off in a different direction from that in a simple valve gear ; but the amount of angular advance will remain the same in both cases. In order to point out clearly the reason why this should be so, we have illustrated in Fig. 197 two connections between the valve and eccentric. 1st. The upper connec- tion, marked " Case 1," is that in which no rocker is employed. 2d. The lower connec- tion, marked " Case 2," is that in which a rocker is interposed. In Case 1 the center C of the crank-shaft is in line with the valve ; in Case 2 the center C 2 of the crank-shaft is situated below the valve so as to admit a rocker. In Art. 61 we have seen that the angular advance of the eccentric is laid off from a line drawn perpendicular to the center line of crank. This method is also applicable to the example now under consideration ; but since this will not give correct results in laying out all valve gears, such as are to be considered hereafter, it will be best first to establish a rule which can be applied to all cases. It is this : RULE 17. The angular advance of the eccentric must be laid off from a line drawn perpendicular to the line of motion of the valve gear (see Art. 63). Hence, before we can comply with this condition so as to find the position of the eccentric in Case 1, or in Case 2, Fig. 197, we must draw the center line of motion of the valve gear. To do this in Case 1, we draw a line L M through the center C of the shaft in a direction in which the valve moves. This line L M will be the center line of motion of the valve in Case 1, and agrees with the definition given in Art. 63. In Case 2 we draw a line L 2 M., through the center C., of the shaft, and tangent to the arc s t, described by the MOIH-:i!.\ I.IH'OMOTH'K CONSTRUCTION center 7? of the lower rocker-arm pin.* This line LI M 2 will be the center line of motion of the valve gear in Case 2. Now let us apply the method given in Art. 61 for finding the position of the eccen- tric in Case 1, Fig. 197. From the center C of the shaft, and with a radius of 2 inches (equal to half the throw of the eccentric in our example), describe a circle fdg; the circumference of this circle will represent the path of the center of the eccentric. Through the center C of the shaft draw a line d e perpendicular to L M. Let A repre- sent the position of the center of the crank-pin when the crank is on the dead center, or, in other words, when the piston is at the beginning of the stroke. Now, since the conditions in our example demand that the center line of the valve gear shall coincide with that of the piston, it follows that the center A of the crank- pin must lie in the line L M and when in this position the valve must have opened the steam port ^ of an inch, which is equal to the given amount of lead and occupy the position as shown in the figure. To find the position of the eccentric which will correspond with that of the valve, and enable the shaft to revolve in the direction indicated by the arrow, we continue our construction as follows : From the center C on the lino L M, away from the crank-pin J, lay off a point h ; the distance between (J and h must be equal to the sum of the lap and lead, namely 1 inch. Through the point // draw a straight line h x parallel to the line d e, cutting the circumference / d g in the point x ; this point x will be the required center of the eccentric, and will travel ahead of the crank ; the valve will open the steam port more and more during the time the shaft revolves through a certain distance, and then close the port, as it should do. In Art. 61 we have drawn the line d e perpendicular to the center line of crank. In this example we have drawn the Hue d e perpendicular to the center line of motion ; but since the center line of crank and the line of motion coincide, the result is the same. The position of the eccentric when a rocker is used, as shown in Case 2, Fig. 197, is found in the following manner : For the sake of convenience and easy comparison, let ns draw the center line of motion L 2 M 2 of the valve gear parallel to L M in Case 1 ; a No let us place the center G' 2 of the shaft in a line drawn through C perpendicu- lar to the line L M, and low enough to admit a rocker with arms each 10 inches long. Let o represent the fixed center of the rocker-shaft, and let the line i k, drawn through o perpendicular to L., M.,, represent the center line of the rocker-arms when these stand midway of their travel, corresponding to the position of the slide-valve when the latter stands in a central position, not indicated in these illustrations. Now, it must be evident that when the valve stands in the position as shown in the figure it has moved 1 inch (the sum of the lap and lead) out of its central position, and consequently the center of the upper rocker-arm pin must have moved out of its central position the same amount in a horizontal direction (not measured on the arc described by the center of the pin), and therefore the center of the pin will be at /when the valve stands in the position as shown. Through the centers / and o draw a straight line / R, cutting the arc s <, described by the lower rocker-pin, in the point R. This " Drawing this center line of motion tangent t.> the arc described by the lower rocker-arm pin is not absolutely correct, but is near enough, and generally considered so. fur all practical purposes in locomotive cons! met ion, or in engines having eccentric-rods of the ordinary length ; that is, engines not having very short eccentric-rods. 114 MODERN LOCOMOTIVE CONSTRUCTION. point R will be the position of the center of the lower rocker-pin when the upper pin is at I ; and, as will be seen, these pins will then be located in the opposite sides along the line i k ; but the distance between the center H and the line i k will be the same as that between the center I and the line i k, namely, 1 inch, because the rocker-arms are of equal lengths. Also notice that as the pin I travels in the direction of the arrow 2, as it should do, the pin R will travel in an opposite direction, indicated by the arrow 3. When the valve stands in the position as shown, the crank-pin A 2 in Case 2 will be on the same side of the shaft as A in Case 1, and will lie in the line L 2 M z , because, according to the condition in our example, the center line of motion of the valve gear coincides with that of the piston. Therefore the following construction will give us the position of the eccentric to correspond with that of the crank. Through the center C 2 of the shaft draw a line d 2 e 2 perpendicular to L 2 M 2 ; and from the center (7 2 , and with a radius of 2^ inches, describe a circle^ d 2 g 2 ; the circumference of this circle will represent the path of the center of the eccentric. From the center C 2 on the line L 2 M 2 , and towards the crank-pin A 2 , lay off a point h 2 ; the distance between the center C 2 and the point h 2 must be equal to 1 inch, because the horizontal distance between the point _R and the line i A; is 1 inch. Through the point h 2 draw a line h 2 x 2 parallel to the line d 2 e 2 , and cutting the circumference f 2 d 2 g z at the point x 2 ; this point x 2 will be the required position of the eccentric in Case 2 when the crank-pin is at A 2 and the shaft rotating in the direction indicated by the arrow. If in Case 2 we had found the position of the eccentric in precisely the same manner as that em- ployed in Case 1, and had placed the eccentric at y and thus caused the eccentric to travel ahead of the crank as in Case 1, a movement in the wrong direction would have been communicated to the rocker-pin R, which would make the valve close the steam port at this particular time instead of opening the same, as it should do. Also notice that y is one end of the diameter of the circle f 2 d 2 g z , and X 2 is the other end of the same diameter. 132. From this we learn that in a valve gear in which a rocker with arms of equal lengths is introduced the eccentric must be placed in a position directly opposite to that of an eccentric in a valve gear in which no rocker is used ; also, when the amount of lap and lead in Case 1 is the same as that in Case 2, then the angular advance in both cases will be equal, although laid off in opposite directions. When two eccentrics and a link are to be used, as in locomotives, then, in order to find the position of the second eccentric, prolong the line h 2 x 2 so as to cut the circum- ference^ d 2 </ 2 ; this point of intersection will be the center of the second eccentric. (See Art. 99.) POSITION OF ECCENTRICS WHEN A KOCKER WITH ARMS OF UNEQUAL LENGTHS IS USED. 133. In Fig. 197 we have shown the position which the eccentrics must occupy when the lengths of the rocker-arms are equal. If, however, the lower rocker-arm is made either longer or shorter than the upper arm, then the position of the eccentrics on the shaft must be changed from that posi- tion they would occupy when the arms of the rocker are of equal lengths. EXAMPLE 40. The length of the lower rocker-arm is Hi inches ; the length of the MOVERS I.OfOMOTIVK COXSTRVCTIOS. 115 upper arm, inches; throw of eccentric, 5 inches; lap, ft of an inch; lead, ^ of an inch ; the center line of motion of the valve gear coincides with that of the piston; it is required to find the position of the eccentrics. Fig. 19H. Draw the center line / k; this line will represent the center line of the rocker-arms when these stand midway of their travel. On the line i k locate any point o to represent the center of the rocker-shaft. From the center 0, and with a radius equal to 9 inches, describe an arc u v to represent the path of the center I of the upper rocker-pin ; also from the center o, and with a radius equal to 11J inches, describe an arc s t to represent the path of the center of the lower rocker-pin. On the arc u v lay off a point I ; the distance between the line i k and the point I must be equal to the sum of the lap and lead, namely 1 inch, measured on a line perpendicular to i k, and not on the arc r. Through the point I and the center o draw a straight line / R, cutting the arc s t in the point 7?. Draw L M, the center line of motion of the valve gear, perpen- ilicular to the line i k and tangent to the arc s t. On the line L M lay off the center C of the shaft. When the valve stands in the position as shown in the figure, the crank- pin will be at A, or, in other words, the shaft C will be between the crank-pin and the rocker. Through the center 6' draw a straight line de perpendicular to L M; also from the center C, and with a radius equal to half the throw, namely 2 inches, describe a circle ; the circumference of this circle will represent the path of the center of eccen- trics. From the center C and on the line L M lay off a point h ; the distance between these points must be 1J inches ; through the point h draw a line parallel to the line d e, and cutting the circumference fdg in the points # and y. The point x will be the center of the eccentric when the crank-pin A has to move in the direction of the arrow; and the point y would bo the center of the eccentric if the crank-pin A had to move in a direction opposite to that of the arrow. If two eccentrics and a link are to be employed, then one eccentric is placed at x and the other at y. Since the valve has -[{! of an inch lap and ,',, of an inch lead, the linear advance of the valve must be 1 inch; that is, when the valve is in the position as shown, it has traveled 1 inch away from its central position; and since the valve is connected to the upper rocker-arm, the distance between the center I and the line i k was made equal to MODERN LOCOMOTIVE CONSTRUCTION. 1 inch. According to Art. 97, the distance between the line i k and the center K of the lower rocker-pin must be greater than 1 inch, because the lower rocker-arm is longer than the upper one. In our present example the distance between the line i k and the center E is l inches. But the eccentric-rod is connected to the lower rocker-arm, and therefore the distance between the center C and the point h must be 1J inches, as we have made it. Hence, lengthening the lower rocker-arm necessitated an increase in the angular advance. If the lengths of the rocker-arm had been equal, the distance between C and h would have been 1 inch, or, in other words, the centers x and y of the eccentrics would have been placed 1 inch away from the line d e, instead of Ij inches as shown in Fig. 198. In the same manner it can be shown that, when the length of the lower rocker-arm is less than the length of the upper arm, then the angular advance of the eccentric will be less than the linear advance of the valve. From this example we learn that, when the lower rocker-arm is longer than the upper one, the angular advance will be greater than the linear advance ; and when the lower rocker-arm is shorter than the upper one, the angular advance is less than the linear advance in short, the angular advance of the eccentric is equal to the distance between the central position of the lower rocker-pin and that in which it will stand when the piston is at the beginning of the stroke.* POSITION OF THE ECCENTRIC WHEN A ROCKER IS USED AND THE CENTER LINE OP MOTION OF THE VALVE GEAR DOES NOT COINCIDE WITH THAT OF THE PISTON. 134. EXAMPLE 41. The length of each rocker-arm is 10 inches ; lap, f f of an inch ; lead, ^g of an inch ; throw of the eccentric, 5 inches ; center line of motion of the valve gear does not coincide with that of the piston ; to find the position of the eccentric. Fig. 199. In this figure the axis of the cylinder is assumed to be in a line with the center C of the shaft ; that is, if the axis of the cylinder is prolonged towards the shaft, it will pass through the center C. Hence the line N P will be the center line of motion of the piston. Again, when the crank is on a dead center, the crank-pin must lie in this line N P ; and when the valve has opened the steam port -fa of an inch, that is to say, when the valve has -fa inch lead, as shown in the figure, the center of the crank-pin must be at A. Let o represent the center of the rocker-shaft. From the center o, and with a radius equal to the length of the lower rocker-arm, namely 10 inches, describe the arc s t ; also from the center o, and with the same radius as before, describe the arc u v. Through the center C draw the line L M tangent to the arc s t. Then L M will be the center line of motion of the valve gear ; and, as will be seen, the center line of motion L M does not coincide with the center line of motion N P Cases of this kind, in which one end of the center line of motion of the valve gear is depressed, are not of rare occurrence in locomotive construction ; we frequently have to do this in order to give sufficient clearance between the lifting-shaft arms or the link and the boiler when the valve gear is placed in full-gear back. But when this * It should be remembered that increasing' the length of the lower rocker-arm, and leaving the throw of the eccentric the same, the travel of the valve will be decreased. Also by decreasing the length of the lower rocker arm without changing the throw of the eccentric, the travel of the valve will be increased. Therefore care anil thought must be given to the subject when the lower rocker-arm is made longer or shorter than the upper rocker-arm MtlliKHX LOCOMOTIVE COXSTRVCTION. 117 Fig.ZOO expedient is resorted to, we must also make a change in the relative positions of the rocker-arms on the shaft, as shown in Fig. 200. In this figure it will be noticed that the cen- ter lines of the rocker-arms do not lie in one straight line, as shown in all our previous figures, but that these arms incline towards each other. By giving the rocker-arms these posi- tions on tho shaft we will preserve the identity and symmetry of their motion. The relative positions of the rocker-arms are found in the following manner : Through the cen- ter o, Fig. 199, draw a line o k per- pendicular to L M; this line will represent the center line of the lower rocker-arm when it stands midway of its travel. Also through the center o draw the line o i perpendicular to the center line of the valve-rod ; the line o i will represent the center line of the up- per rocker-arm when it stands midway of its travel. The lines o i and o k show the required amount of inclination of the rocker-arms towards each other. To draw the rocker in a position corresponding to that of the valve at the beginning of the stroke, lay off from the line i o on the arc u ?>, towards the valve, a point /; the distance between this point / and the line i o must be equal to the linear advance, namely 1 inch. Through the point / and the center ft draw a straight line lo; this line will be the center line of the upper rocker-arm when in a position cor- responding to that of the slide-valve. From the line o k on the arc s t, and towards the center C of the shaft, lay off a point E ; the distance between the point /.' and the line o k must also be equal to the linear ad- vance (1 inch), because the length of the upper rocker- arm is equal to that of the lower one. The line o R represents the center line of the lower rocker-arm when in a position corresponding to that of the valve. From the center C, and with a radius equal to 2J inches, describe the circle filff ; the circumference of this circle will represent the path of the center of ec- centric. Through the center ('of the shaft draw a 118 MODERN LOCOMOTIVE CONSTRUCTION, line d e perpendicular to the line L M; from the same center C lay off on the line L M, towards the crank-pin A a point h; the distance between the points C and h must be equal to the linear advance (1 inch). Through the point h draw a line x y parallel to the line d e, cutting the circumference / d g at the points x and y. The point x will be the center of the eccentric when the crank-pin A is to travel in the direction of the arrow ; and the point y will be the center of the eccentric when the crank-pin A is to travel in the direction opposite to that of the arrow. If a link is to be used so that the motion of the crank-shaft can be reversed, then the point x will be the center of one eccentric, and the point y the center of the other eccentric. Now notice in this case the angular advance of the eccentric is laid off from the line d e, which is not perpendicular to the center line A C of the crank. From this we learn that the angular advance must be laid off from a line di*awn perpendicular to the center of motion of the valve gear, as stated in Rule 17, and this rule holds true in all cases. On the other hand, the expressions, " the eccentric is set at right angles to the crank," and " the angular advance is laid off from a line drawn perpendicular to the crank," are true only in cases in which the center line of motion L M of the valve gear coincides with the center line A C of the crank. LAYING OUT A LOCOMOTIVE VALVE GEAR. 135. In Fig. 199 we have shown a valve gear without a link. Now, adding a link will not change the position of the eccentrics, neither will it make any difference in the positions of the rocker-arms ; the off-set in the arms and the position of the rocker are not interfered with in fact, no change whatever will be required excepting a change in the length of the eccentric-rods. Hence all the remarks relating to the valve gear shown in Fig. 199 are true also for a valve gear in which a link is used. 136. In regard to the position of the center o of the rock-shaft in any valve gear, it may be said that it is usually located in the most convenient position, which in the meantime will give as long eccentric-rods as possible. Hence we find the rocker placed either in front of the yoke-brace or in the rear of it, as shown in Fig. 29. In either case care must be taken to place the rocker far enough away from the yoke- brace to give sufficient clearance between the latter and the link when hooked up ; again, it often happens that, when we attempt in ten-wheeled engines to place the rocker in front of the yoke-brace, the link will strike the engine truck frame, and under these circumstances we are compelled to place the rocker as shown in Fig. 29. The vertical distance from top of frame to the center of rock-shaft is usually deter- mined by the location of the valve-rod, and when the boiler is set compai-atively low, we may have to lengthen the upper rocker-arms so as to lower the position of the rocker for the purpose of obtaining sufficient clearance between the bottom of the boiler shell and the top of link and hanger when the latter are placed in full backward gear. The preceding remarks indicate that for determining the position of rocker-box computations are not required, but good judgment guided by experience must be exercised. 137. The correct working of the valve not only depends on the correct position of the eccentrics, but it will also depend, when a link is used, on the position of the vi>Kn\ T.ocouoTirE CONSTRUCTION. saddle-pin on the link, the length of the lifting-shaft arms from which the links are suspended, and the position of Ilie lifting shaft. The position of the driving axle in the pedestal will also affect to a small extent the equality of the cut-off, and since this axle is free to move up and down in the pedestal, the question which presents Itself is: Where shall we place the driving axle for the purpose of laying out the valve gear? The axle should be drawn in a position corresponding to that which it will have when the engine is in first-class working order; and this position can be taken from Figs. 271 to 279, in which the positions of axles in the pedestals for different sizes of engines in working order are dearly indicated. After the axle and rocker-box have been located, we are then ready for laying out the valve gear, and in order to show plainly the manner of doing so, we shall take the following example and work out the solution in the same way as many (1 raftsmen will do; the only difference being that the draftsman will work out the whole solution in one diagram, whereas we shall use three to enable us to point out the construction more clearly. EXAMPLE 42. It is required to lay out a valve gear such as is shown in Fig. 29. This gear is to be used on an eight- wheeled passenger engine with a piston stroke of 24 inches. The length of each rocker-arm is 10 inches; throw of eccentrics, 5 inches, which will make the eccentricity equal to 2i. inches ; lap, | inch ; lead, / inch ; length of link, 18 inches ; distance between centers of eccentric-rod pins in link, 12 inches ; length of link-hanger, 13 inches; horizontal distance from the center of axle to the center of rock-shaft, 55 inches ; length of connecting-rod, 84 inches ; axis of cylinder, 14 inches above the center of driving axle when the engine is in good working order. We will also assume that after the driving axle has been correctly drawn in the pedestal, and the rocker properly located, it is found that the vertical distance from the center of axle to a horizontal line drawn through the center of rock-shaft is 6 inches. It is required to find, in the order here given, the off-set in the rocker-arms ; the position of crank-pin for full and half stroke of piston ; the radius of links ; the position of eccentrics ; the length of eccentric-rods ; the position of eccentrics for half strokes of piston ; the position of the saddle-pin on the links ; the position of lifting shaft and the length of the lifting-shaft arms from which the links are suspended. Indeed, it may be said that to determine each one of these particulars is a problem by itself, so that the matter of laying out a valve gear consists of the solutions of a number of simple problems. TO FIND THE OFF-SET IN THE ROCKER-ARMS. 138. Let the point A in Fig. 200A be the center of the driving axle ; through this center draw a vertical line, and make the distance from A to i equal to 6 inches; through the point i draw a horizontal line i o, and make the distance from i to o equal to 55 inches, as given in the example ; the point o will be the center of the rock-shaft. From o, and with a radius of 10 inches, describe two arcs, U Fand S T; through the center A draw a line L M tangent to the arc .S' 7'; this line will be the center line of motion of the valve gear. (See Art. 131.) Through the center () draw a line R perpendicular to L 37; the line O R will be the center line of the lower arm of the rocker when the valve stands in the center of its travel. Again, through draw the 120 MODERN LOCOMOTIVE CONSTRUCTION. vertical line 7; we say vertical, because the valve is supposed to move in a horizontal direction ; if the valve-rod moves in any other direction, then I should be drawn perpendicular to that direction. The line 1 represents the center line of the upper J.C \ f ~-s? A\3 JKC 7- c B Bo B, . o (b n f / R .X Pig. 200 A. T Re " " Fro ^~~ arm of rocker when the valve stands in the center of its travel, then K 11 will be the off-set in the rocker-arms. Prolong I to K, TO FIND THE POSITION OF CEANK-PIN FOE FULL AND HALF STEOKES OF PISTON. 139. According to the conditions given in the example, the axis of the cylinder is to be 1J inches above the center A of the axle ; hence, on the line A i lay off a point at a distance of l inches above A, and through this point draw the horizontal line E F, which will be the axis of the cylinder. From A as a center, and with a radius equal to the length of the connecting-rod, namely, 84 inches, describe a short arc cutting E F in the point B 2 ; this point will be the center of the crosshead pin when midway of its travel. Towards the rear of B. 2 lay off the point B at 12 inches from B 2 ; also lay off the point B 3 towards the front of B 2 at a distance of 12 inches from the latter ; the points B and B 3 will be the position of the center of the crosshead pin when the piston is at the extremities of a stroke. It should be remarked here that the foregoing way of finding the points B and B 3 is correct only when the axis E F of the cylinder and the center A lie in one and the same straight line ; but when these do not lie exactly in the same straight line, as is the case in the example before us, then the construction is not correct, but it is sufficiently close for all practical purposes, in cases in which the axis of cylinder is only 1 inches above the center A of axle. In exti-eme cases, say when the line E F is from 3 to 4 inches above the center A, it is best to find the points B and B 3 accurately, which is done in the following manner: From A as a center, and with a radius equal to the length of the connecting-rod minus the length of the crank, describe a short arc cutting E F in the point B; again, from A as a center, and with a radius equal to the length of the connecting-rod plus the length of the crank, describe a short arc cutting E F in the point B 3 ; the distance from B to B 3 will be the length of stroke of piston, which is a little less than twice the length of crank ; of course the length of crank is the distance from the center of axle to the center of crank-pin. With a radius of 12 inches describe from A the circle C, 0, c, Jc; its circumference will represent the path of the center of the crank-pin. Through A and B draw a straight line, and prolong it to C on the circumference of the circle ; this point C will be the center of the crank-pin when the crosshead pin is at the end B of the stroke. Through A and B 3 draw a straight line cutting the path of the crank-pin at c ; this point will be the position of the crank-pin when the crosshead pin is at the end B 3 MfiriER\ LOCOMOT/TE COXSTIIVCTIOX. 121 of tin- stroke. For laying out the valve gear, it is customary to find the points C and c in a somewhat simpler way namely: through A and 7? 2 draw a straight line cutting the path of the '-rank-pin in the points C and c, which will be the centers of the crank- pin eorresponding to the extremities of the piston stroke. This way of finding the (liters is not quite as accurate as the first method given, but the error is so small that it may be safely neglected. In laying out the valve gear, we have to find aiiothi-r two important positions of the crank-pin, namely, those corresponding to the positions of the piston when it is in the center of each stroke, or, in other words, when tin- erosshead pin is at R 2 . These positions are found in the following manner: From B., as a center, and with a radius equal to A R 2 (that is, the length of the connecting- rod), descril>e an arc cutting the path of the center of crank-pin in the points JC' and c, which will be the required points. Join the points A and (7, also A and Jc, by straight lines ; these lines will be the center lines of the crank corresponding to stroke of the piston ; and the lines A C and A c will be the center lines of the crank when the engine is on its dead centers. From A as a, center, and with a radius equal to of the throw of the eccentric, 2i inches, describe a circle cutting the center lines of the crank in the points 1, 2, 3, and 4. TO FIND THE RADIUS OP THE LINK. 140. According to construction, the point R in Fig. 200A is the center of the lower rocker-arm pin or link-block pin when the valve stands midway of its travel ; hence, according to Art. 123 the radius of the link is equal to the distance A R. If this radius is made either longer or shorter than A R, the tendency will be to produce an unequal lead when the link is placed in mid-gear. TO FIND THE POSITIONS OF THE ECCENTRICS FOR FULL STROKES OF PISTON. 141. This construction is shown in Fig. 200B, which, for the sake of clearness, is drawn to a larger scale than Fig. 200 A, but in both figures the lines and points which have the same letters affixed represent the same parts of the valve gear. On the line L M lay off from A a distance A p equal to the sum of the lap and lead, H inch, and through the point /, draw a line X 7 perpendicular to L M cutting the circle 1, :;. 4. in th- points X and Y-. tin- j^iut A", a--ording to Art. 131, will be the center of the forward e<-,-entrie ; and Twill be the center of the backward 122 MODERN LOCOMOTIVE CONSTRUCTION. eccentric when the crank-pin is at C. In this case we have made A p equal to the lap and lead, because the lengths of the rocker-arms are equal. (See Art. 131.) If the lower rocker-arm had been longer or shorter than the upper one, then the distance A p would have been made respectively greater or less than the sum of the lap and lead. (See Art. 132.) On the line L M lay off from A a distance A q equal to A p, and through the point q draw a line x y parallel to X F, cutting the circumference 1, 2, 3, 4, in the points x and y. The point x will be the center of the forward eccentric and y that of the backward eccentric when the crank-pin is at c. Here, then, we have found the position of eccentrics when the engine is on its dead centers. TO FIND THE CORRECT LENGTH OF ECC3NTRIC-RODS. 142. For this purpose we shall need a template. Let Fig. 200C represent the link. Cut out a template represented by the shaded portion of this figure. The edge r s of the template must coincide with the link arc ; and the arc t u of the template must pass through the centers of the eccentric-rod pins. Through the centers of the eccentric-rod pins t and u draw straight lines on the tem- plate, and also through a point midway between these centers draw on the template a line v w towards the center from which the link has been drawn ; the lines through t and u may be drawn parallel to v ^v, or they may also point to the center from which the link has been drawn ; either way will answer the purpose, so long as the points t, v, and u on the concave edge of the template are correctly located as explained. Pfg. 200 a From the points X and x as centers (Fig. 200B), and with a radius equal to A R minus the width of v w, draw two arcs X } and x } above the line L M] and with the same radius draw from the centers Fand y two arcs 1", and ?/,, below L M. Now place the template with its center line v w on L M, and with its points t and on the arcs X, and F, respectively, and along the edge r s draw an arc on the paper. Again, place the template with its center line v w on L M, and with its points t and u on the arcs #, and T/J respectively, and along the edge r s draw another arc r z s 2 . If now these two arcs which have been drawn along r s are at equal distance from the point 72, then the line drawn from X to t or from Y to u will be the correct length of the eccentric- rod ; but the chances are that the arcs drawn along r s will not be at equal distances from .R, because in one position the eccentric-rods will cross each other, and in the other position they will not do so, and for these conditions we have not made any allowance. We must therefore draw another set of arcs Xj Y l and x l and ?/ with a somewhat larger radius, and again place the concave side of the template on these arcs and draw arcs along the edge r s as before. With a little care and good judgment in drawing X t , F ]; x^ and y lt the arcs drawn along the edge r s of the template will now be at equal distances from the point jR, and therefore the lines joining the points X and t or Y and u will be the correct length of eccentric-rods. 143. The heavy lines X t and Y u represent the position of the center lines of the eccentric-rods when the crank-pin is at (7; it is seen that these rods cross each other; but when the crank-pin is at c the eccentric-rods will not cross each other ; they are then said to be " open." If we connect the rods so that they will not cross each other MODERN LOCOMOTIVE CONSTRUCTION. 123 when tin- crank-pin is at (7, we shall have no lead when the link is placed in mid-gear, and this is not admissible iu locomotive practice, although it may be advantageously employed in hoisting engines, because when there is no lead with the link in mid-gear the engine can be stopped simply by raising the link without touching the throttle- valve. TO FIND THE POSITION OF ECCENTRICS FOR HALF STROKES OF PISTON. 144. To show this construction we shall refer to Fig. 200D, to which nearly all the lines shown in the former figure have been transferred. We have seen that the center lines of the crank corresponding to full and half stroke of piston cut the path of the center of eccentrics in the points 1, 2, 3, and 4. Now when the crank-pin is at C the forward eccentric will be at X, and the length of the arc from the point 1 to X is fixed ; it cannot be changed in whatever position the crank may be ; hence, when the crank-pin is at J 6' the arc from the point 2 to X must be equal to that from 1 to X. Therefore, making the arc JX-2 equal to X-l, we obtain the point X, which is the center of the forward eccentric when the piston is in the center of the forward stroke. For similar reasons we make the arc Ja>4 equal to X-l ; the point ^x will be the center of the forward eccentric when the piston is in the center of its return stroke. Of course, care must be taken to lay these points off on the path of the center of eccentrics, that is, on the circumference X Y x y, and these points should be laid off to follow the crank. We know that the point Y is the center of the backward eccentric when the crank is at C, and the length of the arc from 1 to Y remains fixed for all positions of the crank ; therefore make the arc %Y-2 equal to Y-i, also make the arc / 4 equal to the same arc; of course, the points ^Y and %y must be ahead of the crank. Now the point %Y will be the position of the backward eccentric when the piston is in the middle of its forward stroke, and the point \y will be the position of the backward eccentric when the piston is in the middle of its return stroke. TO FIND THE CENTER OF THE SADDLE-PIN. 145. From the centers iX and 4.r, ami with a radius equal to X t or Y u (Fig. 200B), describe in Fig. 200D above the line L 3/the arcs i A, and i./, ; from the centers A I'aml 124 MODERN LOCOMOTIVE CONSTRUCTION. %y, and with the same radius, describe below the line L M the arcs Y } and %y } . It will be remembered that the point E is the center of the link-block pin when the valve stands midway of its travel ; from this point E as a center, and with a radius equal to the lap of valve of an inch, describe the lap circle, cutting the line L M in the points a and b. Now place the template with its point t on the arc X,, and with the point u on the arc &Y U and its outer edge r s touching the point a; in this position draw on the paper along the outer edge of the template an arc r s, and also mark off the points v and w ; lift off the template, and through the points v and w draw a straight line v w ; this line represents the position of the center line of the link when steam is being cut off at J of the forward stroke. Again, lay the template in a position as indicated by the darker shading; the point t must lie on the arc \x-; the point , on the arc ?/, ; and its outer edge r 2 s 2 must touch the point b. In this position draw on the paper an arc r 2 s 2 along the outer edge of the template, and also mark off the points v 2 w z ; then lift off the template and join the points v 2 w 2 by a straight line ; this line will be the center line of link when steam is cut off at \ of the return stroke. On the line v w lay off a point f, and on the line v., iv z lay off a point / 2 , to comply with the follow- ing conditions : The distance from the point f to the arc r s must be equal to the distance from the point f, to the arc r 2 s 2 , and these points f, f, must also lie in a line parallel to L M ; the position of these points are found by trial usually two or three trials will locate them correctly. The distance from the arc r s to the point f, or the distance from the arc r 2 s 2 to the point f 2 (these distances being equal), will be the amount that the saddle-pin has to be set inwards from the link arc. Mark off correctly this point /on the template. TO LOCATE THE LIFTING SHAFT. 146. On the line L M lay off from E a point c 2 ; the distance from E to c 2 must be equal to the sum of the lap and lead If inches. Also from E lay off on L M a, point c 3 ; the distance from E to c.j must again be equal to the sum of the lap and lead. Let it now be remembered that the arcs Xj, F 1? x l and y l in Fig. 200D represent the same arcs as those which have the same letters affixed in Fig. 200B. Now place the template as low as possible, with its point t on the arc X 19 the point u on the arc Y ly and the outer edge r s touching the point c 2 . In this position prick off through the point / on the template the point d on the paper. Now move the template to as low a position as possible, so that its outer edge r s will touch the point c :j with the point t on the arc # and the point u on the arc y lt and in this position prick off through /on the template a point e on the paper. From the points d and e as centers, and with a radius equal to the length of the link-hanger, 13 inches, describe two arcs intersecting each other in the point k. Now move the template as high as possible, and let its outer edge r s touch the point c 2 , and let the point t be on the arc X 1? and the point u on the arc Y lt then through the point /on the template prick off on the paper a point g. Again, move the template to as high a position as possible, and let its outer edge r s touch the point r 3 , and let the point t be on the arc x^ and u on the arc ?/, ; through / on the template prick off on the paper a point 7). From the points g and h as centers, and with a radius equal to the length of the link-hanger, describe two arcs intersecting each other 3TODKRX LOCOMOTIVE COXSTRVCTIOX. in the point n. Lastly, from tho points / and f., previously located on the paper, describe with a radius of 13 inches two arcs intersecting each other in the point I. Now find by trial a point m from which an arc passing through the points kin can lie described; this point / will be the center of the lifting shaft, and the radius m n will be the length of the lifting-shaft arms from which the links are to be suspended. This completes the whole construction. It will be noticed that in this valve motion the valve will have equal lead at full stroke, and cut off steam at the center of the forward and return stroke. Under these conditions steam will be cut off at equal portions of the forward and return strokes, or very nearly so, for all intermediate positions of the liuk. 147. lu designing an engine the foregoing construction is essential ; it gives us the required data for several details which can be made and completely finished before they are sent into the erecting shop. But there are other details which have to be adjusted to the imperfect workmanship which cannot always be avoided; for instance, the length of eccentric-rods will have to be adjusted under the engine, also the eccentrics will have to be set on the axle, and there are other points which cannot be exactly transferred from the paper to the engine ; it will therefore be advantageous to examine now the mode of procedure in setting the valves on the engine in the shop. PEACTICAL EXAMPLE OF SETTING THE VALVE GEAK OF A LOCOMOTIVE IN THE ERECTING SHOP. EXAMPLE 43. Throw of the eccentric is 5 inches; lap, }- of an inch; lead, -j 1 ,, of an inch ; clearance between piston and each cylinder head is j} of an inch ; type of locomotive is one in which the eccentrics are placed on the main axle, that is, the axle to which the main rod is connected : it is required to set or adjust the valve gear. In this example the position of the saddle-pin on the saddle is assumed to be correct, so that in setting the valve gear no loose saddle is to be used. To the young mechanic, it may appear that setting the valve gear of a locomotive is a very mysterious and difficult operation. Yet, if he understands the theory of the valve motion, which we have endeavored to explain and to make plain in the foregoing .irticles, and proceeds in setting the valve gear in a systematic manner, this opera- tion will lose all its mystery, and will not be such a difficult problem as it first appeared to be. True, in attempting to set the valve gear we are confronted with that which may seem to be a very mixed-up problem, because the correct position of the eccentrics on the axle and the exact length of the eccentric-rods must be determined ; and since these two items are intimately connected, we may often be in doubt as to which of the two has been correctly found. But by dividing this problem into a number of simpler ones, its solution will be comparatively easy. In connection with the setting of the valve gear a few preliminary preparations are necessary; this whole subject will be treated in the following order: 1st. Blocking up the main axle boxes in the pedestals of the frames. 2d. To find the exact position of tho crank-pin when the piston is at the beginning of a stroke. 3d. To lest the amount of clearance between the piston and cylinder heads. 4th. To connect the eccentric-rods correctly to the liuk. 126 MODERN LOCOMOTIVE CONSTRUCTION. 5th. To find the correct length of the eccentric-rods. 6th. To find the correct position of the eccentrics on the axle. 7th. To lay off the notches in the reverse arcs or quadrants. In this example it is assumed that the quadrants are properly fastened in their position, and that they have no notches. Also that the reverse lever and lifting shaft are in correct positions ; and that the reach-rod connects the reverse lever and lifting shaft ; and lastly, that the links are suspended from the lifting-shaft arms, and that the former are properly attached to the lower rocker-arms; and also, that the connections between the upper rocker-arms and the valves are complete. BLOCKING UP THE MAIN AXLE BOXES IN THE PEDESTALS OF THE FKAMES. 148. The locomotive should rest securely on blocks, so that the main driving wheels can be lifted off the track and held in a position which will allow the main driving wheels to be easily turned around in their boxes. In lifting the main driving wheels off the track, they should be raised to a position in the pedestal which corre- sponds to the position of their boxes in the frame when the engine is hauling a train. The general practice is to give l inches clearance between the axle box and pedestal cap, and about 3 inches clearance between the top of axle box and frame. In smaller engines whose axle boxes have less clearance in the pedestals, the proportion between the upper and lower clearances should be about the same as that just given ; namely, the clearance on top of the axle box should be about twice as great as that below the box. (See Figs. 271 to 279.) If then 1J inches is to be the clearance at the bottom, blocks each l inches thick are inserted between the main axle boxes and the pedestal caps, which will hold the main driving wheels off the track and in the correct position during the time the valve motion is to be adjusted. No attention need be paid to the other boxes and wheels, since in this class of engines it is not necessary to put on the side rods for the purpose of setting the valve gear ; in fact, the side rods would be in the way, and would give unnecessary labor in revolving the main driving wheels. TO FIND THE EXACT POSITION OF THE CRANK WHEN THE PISTON IS AT THE BEGINNING OF A STROKE; OR, IN OTHER WORDS, TO LOCATE THE DEAD CENTERS OF THE CRANK. 149. Tig. 201. The following remarks refer only to the setting of the valve gear on the right-hand side of the engine ; the manner of setting the valve gear on the left-hand side of the engine is precisely the same as that adopted for the right-hand side. First set or adjust one side, and then the other side. On the face of the tire describe with the aid of a gauge two arcs d e and / g in about the same relative positions to that of the crank, as shown in the figure ; care should be taken to describe these arcs as true as if they had been described in the lathe. Attach the main rod to the crank-pin and crosshead ; but at present do not fasten the piston-rod to the cross- head. Now turn' the driving wheel in the direction of the arrow until the crosshead is within a short distance from the end of the stroke, say \ an inch; while in this position mark on the slides a line i even with the end,/ of the crosshead. Also, while the wheel and crosshead are in this position, place a center punch mark c on the side LOCOMOTICK COXSTKI : CI'I<>.\. 127 of the fire-box or any other convenient fixed piece of mechanism. From this point c as a center, and with a tram of any convenient length as a radius, de- srribe on the face of the tire a short a iv, cutting the arc d e (previously marked on the tire) at the point d (this point d will at this instant coincide with the end h of the tram, and not as shown in the figure). Now turn the wheel in the same direction as before, causing the crosshead to complete its full stroke and a very small portion of its return stroke; and when during this motion the edge j of the cross- head touches the lino i on the slides, stop turning the shaft, and while in this position describe from the center punch mark c as a center, and with the same tram as before, a short arc on the face of the tire, cutting the arc d c at the point e. Midway between the points d and e on the arc d e lay off point It. Turn the wheel in a position in which the tram will touch the points c and h the crank-pin will then be at B, and the piston will be. at the beginning of its forward stroke ; or, in other words, the crank will then be on one of its dead centers. While the crank stands at J> draw on the slides a line /, even with the end j of the crosshead ; this line k will indicate the end of the stroke that is, the end ./ of the crosshead will not travel beyond the line /, with the con- necting-rod attached. In order to locate the other dend center .1 wo again turn the wheel in 128 MODERN LOCOMOTIVE CONSTRUCTION. the direction of the arrow until the crosshead is within a short distance of the front end of the stroke, say an inch, and while in this position mark on the slides a line m even with the end n of the crosshead ; also, before the wheel and crosshead are moved out of this position, describe on the face of the tire from the point c as a center, and with the same tram as used before, a short arc, cutting the arc fg at the point g. Next turn the wheel in the same direction as before, causing the crosshead to com- plete its forward stroke and a small portion of its backward stroke, and when the edge n of the crosshead again touches the line m on the slides, stop turning the wheel. From the center c, and with the same tram, describe on the face of the tire a short arc, cutting the arc fg at the point/ Mark off the point I on the arc fg midway between the points /and g. Now, turning the wheel in a position in which the tram will touch the points c and I, the center of the crank-pin will be at A, which is the other dead center. While the crank-pin is at A draw on the slides a line o even with the end n of the crosshead ; this line o will indicate the other end of the stroke. TO TEST THE AMOUNT OF CLEARANCE BETWEEN THE PISTON AND CYLINDER HEADS. 150. For this purpose we must take off the main rod, fasten the piston to the piston-rod, key the piston-rod to the crosshead, and bolt the cylinder heads to the cylinder. Our example calls for f of an inch clearance between piston and cylinder head at each end of the cylinder. Consequently the crosshead with piston-rod and piston must be pulled out as far as can be done ; if then the edge j of the crosshead overlaps the line k, $ of an inch, the clearance is correct ; if the edge j of the crosshead only reaches of an inch beyond the line &, then the clearance is of an inch too small ; or if the edge j of the crosshead does not reach the line k, then there is no clearance, and the cylinder heads are liable to be broken if we attempt to turn the crank over the dead centers. In a similar manner we find the amount of clearance at the front end of the cylinder ; that is, we push the crosshead towards the front as far as it will go, then, if the edge n of the crosshead moves of an inch beyond the line o, the clearance is correct; if less, the clearance is insufficient. If the clearance is insufficient at the back end of the cylinder, then a corresponding amount must be turned off the back cylinder head. An insufficient clearance at the front end may be caused by the heads of the follower bolts projecting too far beyond the piston ; in that case a groove must be turned in the front cylinder heads, to clear the heads of the follower bolts ; or the insufficient clearance may be caused by the front cylinder head projecting too far into the cylinder ; in this case a sufficient amount must be turned off the front cylinder head. In some cases an insufficient clearance may be caused by the piston being fitted out of square on the piston-rod ; in that case the faces of the piston must be turned off. The writer in his experience has seldom found the clearance to be too great, but has often found it to be too small, generally owing to the rough- ness of the faces of the piston and inside surface of the cylinder heads, as these are seldom turned unless it is absolutely necessary to do so for the correct amount of clearance. M<H>i:i;.\ l.ornMilTlfK CONSTRUCTION. TO CONNECT THE ECCENTRIC-RODS CORRECTLY TO THE LINK. 151. In locomotives it is necessary to preserve the lead, no matter in what position the link may be placed. In Art. 108 we have shown that the eccentric-rods can be connected to the link in a manner which will increase the lead as the link is moved from full-gear to mid-gear. In Art. 110 it is also shown that the eccentric-rods can be connected to the link in a manner which will give lap instead of lead when the link is in mid-gear. Now, since we must have lead in whatever position the link may be placed, it follows that the eccentric-rods must be connected to the link in a manner which will accomplish the desired result. In Fig. 201 the piston is at the beginning of its forward stroke, and the eccentric-rods are shown to cross each other, and, conse- quently, when the axle has made one-half of a revolution, and the piston is at the begin- ning of the backward stroke, the eccentric-rods will not cross each other, as shown in Fig. 29 (Art. 52). This manner of connecting the eccentric-rods to the link is correct, because it will give lead, no matter in what position the link is placed, although in mid- gear the lead will be greater than in full-gear. (See Art. 108.) The reason why the manner of connecting the eccentric-rods to the link should affect ^the lead is clearly shown in Fig. 202. In this figure the different parts of the valve gear are represented by center lines ; the arc d I represents an arc drawn through the center of the link opening, and the arc e g represents the arc in which the centers of eccentric-rod pins arc located. The full lines show the correct manner of connecting the eccentric-rods to the link, and the dotted lines represent the incorrect manner of doing this. Here it will be seen that by connecting the eccentric-rods, as shown by the full lines, we have lead when the link is placed in mid-gear ; and by changing the connections, as shown in dotted lines, we push the lower rocker-arm pin away from the axle, which causes the upper rocker-arm pin to pull the valve towards the axle, and thus close the port and destroy the lead when the link is in mid-gear. In connecting the eccentric- rods to the link, as shown in Fig. 201, we must not forget that a rocker is employed. If a rocker had not been interposed, then the eccentric-rods would not cross each other when the piston is at the beginning of the forward stroke, but would be open, as shown in Fig. 1G8 (Art. 108). TO FIND THE CORRECT LENGTH OF THE ECCENTRIC-RODS. 152. Fig. 203, to which we now shall refer, is supposed to represent the same valve gear as that shown in Fig. 201. But for the sake of clearness we have left out all details not necessary for a clear conception of the subject. For instance, instead of showing the driving wheel with arms and crank, as has been done in Fig. 201, we have simply shown the tire of the same driving wheel with the arcs <i h c and//// marked ii] ton its face. Of course, these arcs represent the same arcs as shown on the face of tire in Fig. 201. In Fig. 203 the center line of crank is represented by the straight line B 6' or A C; B being the center of crank-pin when it is on the rear dead center, and A the center of crank-pin when on the front dead center; (! is the center of the driving axle. The circumference x // represents the path of the centers of eccentrics. The distance between the rocker and the slide-valve has been shortened and the slide-valve 130 MODERN LOCOMOTIVE CONSTRUCTION. I drawn to a larger scale than the other details. The slides have been left out, because for the present purpose no attention need be paid to them. The tram c h, the reverse lever H, the quadrant G, reach rod, and lifting shaft represent the same details as those shown in Fig. 201. Also, the cen- ter punch marks c in Figs. 201 and 203 represent one and the same point. Drawing a part of Fig. 203 to a larger scale than the other part will not affect the correctness of the following reasoning and explanation : In order to save as much time and labor as possible when the correct length of each eccentric- rod is to be determined, it will be best to obtain from the drawing-room the correct relative posi- tion of the eccentrics to that of the crank, also the length of the eccentric-rods ; and then first set the eccentrics on the driving axle in a position which appears to be sufficiently accurate, or, in other words, set the eccentrics on the axle as nearly cor- rect as can be done without spending too much time, or making special measure- ments. Also adjust the length of the eccentric-rods to the length obtained from the drawing-room, and bolt the rods to the eccentric- strap, and connect the rods to the link as previously explained. Now, the eccentric-rods being properly connected to the link, our next step will be to find the correct elevation or location of the link, and the position of the reverse lever // when the valve motion is in full-gear forward, and also in full-gear backward. The general practice is to suffi- ciently raise or lower the link which will not allow the link- block to approach the ends of the slot in the link closer than or jj of an inch during any one stroke. Hence, we may say the least clear- ance between the link-block and the link is from f to an inch. MODERN LOCO.VOTIJ'E CONSTRUCTION. us assume that this clearance is to be % an inch. Hence, turn the driving wheel in the direction of the arrow 1 (Fig. 203), and in the meantime move the reverse lever H into the forward gear, and when the lever is in a position which will cause the least clear- ance between the top of the link-block and the end of the slot in the link, during one revolution of the wheel, to be equal to an inch, stop turning the wheel and clamp the lever // to the quadrants G. This location of the link will be that to which it must be lowered when the valve motion is in full-gear forward ; and since the elevation or location of the link is regulated by the reverse lever //, it follows that the position of the lever H as found is for full-gear forward. Therefore on the quadrants G mark this position of the reverse lever //, so that at any time afterwards it can again be readily placed in the same position. Next turn the wheel in a direction opposite to that of the arrow, and in the meantime move the reverse lever H towards the rear end of the quadrants G, and when the link is sufficiently raised so as to cause the least clearance between the bottom end of the link-block and end of the slot in the link to be equal to % an inch during one revolution of the wheel, stop turning the same, clamp the lever //to the quadrants G, and mark its position on the quadrants for future use. Now, to determine the length of the eccentric-rods, we simply lengthen or shorten the rods so that the distance between the forward end s of the extreme travel of the slide-valve and the outer edge r of the front steam port will be equal to that between the rear end s 2 of the extreme travel of the valve and the outer edge t of the rear steam port. In adjusting the length of the eccentric-rods, we may commence with the forward or back- ward eccentric-rods ; let us commence with the former. Place the reverse lever H and thus the whole valve motion into the full forward gear, and clamp the lever H to the quadrants G. Place a small ordinary square against the edge p of the slide-valve ; then turn the driving wheel in the direction of the arrow 1, causing the slide-valve to move in the direction of the arrow marked 2, and pushing the small square before it. When the valve has reached its extreme end s of travel, the valve will commence to move in an opposite direction, as indicated by the arrow 3, and the square will be left standing, indicating the distance between the outer edge r of the front steam port and the extreme end s of the travel of the valve. "While the square is in this position draw on the steam-chest seat a line touching the edge s of the square. Next place the squar< against the edge o of the valve, and continue turning the driving wheel in the same direction as before, causing the valve to travel in the direction of the arrow 3, and pushing the square towards the rear end s., of the travel. When the valve has pushed the square towards the rear as far as it can do, draw on the steam-chest seat a line touching the edge s 2 of the square; this line s 2 indicates the rear end of the extreme travel of the valve, and the distance s 2 t shows the amount of travel of the valve beyond the outer edge t of the rear steam port. If the distance s 2 t is equal to the distance r s, the length of forward eccentric-rod is for the present considered to be correct. If r sis greater than s 2 t, the eeeontrie-rod is too short and must be lengthened ; if r s is less than s. 2 t, the eccentric-rod must be made shorter. Now place the reverse lever /JTinto full-gear backward, and damp it to the quadrants G. Turn the wheel in a direction opposite to that of the arrow 1, and with the aid of the small square find tit-- extreme travel of the slide-valve in a manner precisely the same as that just explained. And if in this case the distances s., t and r s are equal, the length of the 132 MODERN LOCOMOTIVE CONSTRUCTION. backward eccentric-rod is for the present considered to be correct. If these distances s 2 t and r s are not equal, the backward eccentric-rod must be lengthened or shortened as the case may require. If the backward eccentric-rod has to be lengthened or shortened, the valve motion should again be set into full-gear forward and examined, so as to determine that the adjustment of the length of the backward eccentric has not affected the action of the forward eccentric-rod. It is possible that the length of the forward eccentric-rod may want a little readjustment. TO FIND THE CORRECT POSITION OF THE ECCENTRICS ON THE AXLE. 153. Place the reverse lever H into full-gear forward ; turn the driving wheel in the direction of the arrow 1, Fig. 203, till the tram will touch the center punch marks c and h, and then stop turning the wheel. When the wheel is in this position, the crank-pin will be on the rear dead center B. Move the forward eccentric around the driving axle until the required lead is obtained that is, until the valve has opened the rear steam port i a 6 of an inch. Again, turn the driving wheel in the same direction as before, till the tram will touch the center punch marks c and I ; then stop turning the wheel. While the wheel is in this position, the crank-pin will be on the front dead center A. And if now the workmanship of the valve gear is absolutely perfect, the lead, when the crank is in this position, will also be i^ of an inch. But to obtain such workmanship is very difficult, if not impossible, and therefore it must notlje surprising to find the lead at the front end of the cylinder to be somewhat incorrect. Assume the lead at the front end is of an inch, and at the back end n, of an inch. Now, since, according to our example, n, of an inch is the required lead, and since the lead at both ends of the cylinder must be equal, it follows that the lead at the front end must be reduced, without changing the lead at the back end of the cylinder. To do this we must shorten the forward eccentric-rod ^ of an inch, and move the center x of the eccentric towards the center line B C of the crank, until the valve has just opened the front steam port rg of an inch. Turn the driving wheel once or twice around its axis and examine the lead ; if the lead is equal to n, of an inch at each end of the cylinder) consider, for the present, the setting of the forward geaj* to be correct. Next move the reverse lever // into full backward gear, and find the correct position of the backward eccentric y in a similar manner to that adopted for finding the position of the forward eccentric x. In finding the position of the backward eccentric y or setting the back- ward motion of the valve gear, the driving wheel should always be turned in a direction opposite to that indicated by arrow 1. Now put the valve motion in full-gear forward, and see that the adjustment of the backward gear has not deranged the valve motion when in the forward gear. Perhaps a little readjustment will be necessary ; if so, the valve motion will generally indicate where the readjustment is to be made. When the valve motion is in the forward gear, the driving wheel should always be turned in the direction of the arrow 1 never in the opposite direction. Should the wheel be turned a little further than was intended, we must either turn the wheel completely around its axis, or turn it back considerably beyond the stopping point, and then turn slowly and carefully in the direction of the arrow 1, until it arrives at the stopping point. By so doing, any slack motion which may exist will not interfere with the correct MODERN LOCOMOT1TK CONSTRUCTION. 133 set ti iiir <>t' the valve motion. If now it is foimd that the lead is ,- of an inch at each end of the cylinder when the valve motion is in full back- ward gear, and also in full forward gear, the set- ting of the valve gear is correct and complete. Since we have assumed that the position of the saddle-pin <>M the saddle is correct, and that the location of the lifting shaft and reverse lever is also correct, according to drawing received from the drawing-room, the slide-valve will cut off equal portions of steam at each end of the cyl- inder. TO LAY OFF THE NOTCHES IN THE QUADRANTS. 154. Iii Fig. 204 we have represented the same mechanism as that shown in Fig. 201, but for the sake of clearness some of the details have been left out. In Fig. 204, the line k on the rear end of the slides represents the extreme end of the travel of the crosshead end j t and the line o on the front end of the slides represents the extreme end of the travel of the crosshead end n. It is now to be shown how the notches on the quadrants G can be located, so that when the reverse lever latch L is placed in one of these notches steam will be cut off when the cross- head is in a corresponding given posi- tion between the lines k and o marked on the slides. For this purpose we must attach the conneefcmg-rod to the crank-pin and crosshead, so that when the wheel is in motion the crosshead will also be in motion. In Art. 130 we have seen that there are two ways of arranging the notches in the quadrants (I, namely: 1st. The notches may be cut = as close together as the strength of material will allow. 2d. The notches may be cut so as to hold the reverse lever in positions which will cause the steam to be cut off 134 MODERN LOCOMOTIVE CONSTRUCTION. in the cylinder at some full number of inches in the stroke. We will first consider how to locate the notches in the quadrants when steam is to be cut off at a number of full inches in the stroke. Assume that the stroke, in Fig. 204, is 24 inches, and that steam is to be cut off when the piston has traveled 6, 8, 10, 12, and 15 inches from the beginning of the stroke ; it is required to find the positions of the notches in the quadrants G, and also, as is always customary, find the center notch which will hold the valve motion in mid-gear. In Art. 152 we have shown how to locate the notches for full-gear forward, and also for full-gear backward ; it now remains to be shown how to locate the intermediate notches. First, let us find the location of the center notch, or, in other words, the notch which will hold the valve motion in mid-gear. To do this move the reverse lever H (Fig. 204) towards the middle of the quadrants G, and in the meantime turn the driving wheel in the direction of arrow 1 that is, in the direction of the for- ward motion of the wheel ; also watch the movement of the slide-valve. When finally the reverse lever H arrives in a position in the central portion of the quadrants which gives the shortest travel to the slide-valve, the reverse lever is then in the desired position, and will hold the whole valve motion in mid-gear, and the latch of the reverse lever will indicate the position of the center notch ; therefore on the arcs G scribe off the end of the latch L, and to these marks the center notch must be cut. To locate the other notches lay off on the slides a number of fine and dis- tinct lines, as represented in the figure by the lines marked 6, 8, etc.; in scribing these lines on the slides care should be taken not to disfigure them. The first line, marked 6 in our figure, must be 6 inches from the line k ; the second line, marked 8, must be 8 inches from the line k; and the third 10 inches from A'; and so on for all the given points of cut-off. Now turn the driving wheel in the direction of the arrow 1, causing the crosshead to move away from k ; as soon as the edge j of the crosshead touches the line marked 6, stop the motion of the wheel, and then slowly move the reverse lever H from the center notch towards the forward end of the quadrants G until the slide-valve has just closed the rear steam port ; then on the arcs mark off the end of the latch, and thus locate the notch which will hold the valve motion in a position that will cut off steam at 6 inches from the beginning of the stroke. Again, turn the driving wheel in the direction of the arrow 1, and when the edge j of the crosshead touches the line marked 8 on the slide, stop the motion of the wheel, and then move the reverse lever towards the forward end of the quadrants until the slide- valve has just closed the rear steam port ; then again, on the quadrants, mark off the end of the latch L and thus locate the 8-inch notch. In a similar manner the locations of all the other notches in the forward gear are obtained. In this example we have assumed that the valve motion has been correctly designed in the drawing-room, and also correctly put up in the erecting shop, and consequently we do expect that, when the driving wheel moves in the direction of arrow 1, and the crosshead in the direction of the arrow 2, and the reverse-lever latch is in the notch marked 6, the valve will close the front steam port when the crosshead edge n has moved 6 inches away from the line o, which was previously marked on the slide ; or when the latch is in the notch marked 8, the valve will close the front steam port when the crosshead edge n has moved 8 inches from the line o. MODERN LOCOMOTIVE CONSTRUCTION. 135 To lay off the notches for the backward motion a similar method is pursued, and the same lines indicating the points of cut-off previously described on the slides, and used for the forward motion of the valve gear, can also now be used for the backward motion. Hence, to lay off the notches for the backward motion, again place the reverse lever // in the center notch, and place the wheel in a position in which the edge j of the crosshead will touch, or nearly so, the line k on the slides. Then turn the driving wheel in a direction opposite to that of arrow 1, and when, the edge j of the crosshead touches the h'ne marked 6 on the slide, stop the motion of the wheel, and move the reverse lever H towards the back end of the quadrants, until the slide- valve closes the rear steam port ; then mark off on the quadrants the end of the latch, thus obtaining the location of the 6-inch notch for the backward motion. In a similar manner the position of all the notches in the backward gear are obtained; and since we have assumed that the valve gear has been correctly designed, it is expected that when the reverse lever latch is in the 6, 8, or 10 inch, etc., notches steam will also be cut off at 6, 8, or 10 inches when the crosshead travels in the opposite direction, namely, in the direction of arrow 2. Of course, a perfect, equal cut-off is hardly to be expected ; that is, when the crosshead moves in the direction of arrow 3, and steam is cut off at 6 inches, it is not to be expected that steam will also be cut off at 6 inches when the crosshead moves in the direction of arrow 2 ; but we do expect that, as long as the reverse-lever latch remains in one notch, the points of cut-off will not vary more than J of an inch. If the difference is greater than J of an inch, an inaccuracy exists in the fitting up of the valve gear, or it is due to a faulty construction ; in either case it should be rectified. The notches must be correctly located for both cylinders, so that when steam is cut off at 6, 10 inches, etc., in one cylinder the steam must be cut off at the same points in the other cylinder, or, in other words, both cylinders must receive the same amount of steam. Hence, after the notches have been correctly located for one cylin- der, we must test their accuracy for the other cylinder; and if then one cylinder receives more steam than the other, we generally find that the cause for this inac- curacy is in the position of the lifting-shaft arms, which are out of line that is, one of the arms may hold the link too high or too low, and consequently this arm must be sprung into the proper position, which is often accomplished while the shaft is cold, without taking it out of the engine. When steam is to be cut off equally without regard to any particular points of cut-off or full number of inches in the stroke, the notches are spaced off evenly be- tween the two outside ones and as close together as the strength of the material will allow, and therefore generally have an inch pitch that is, J an inch from center to center of notch. (See Art. 130.) In this case also the same care must be taken to arrange the valve motion in a manner which will supply both cylinders with tlie same amount of steam. It should be remembered that the foregoing instructions in setting the valve gear are intended for new work only. When the valve gear for an old engine is to be readjusted, the wear of the different parts must lie taken into consideration, which sometimes makes the readjustment a difficult process. re<|uiring experience and a knowledge of the principles connected with the design of the valve motion. 136 MODERN LOCOMOTIVE CONSTRUCTION. REMAKES KELATING TO THE VALVE MOTION IN WHICH THE ECCENTRICS ARE NOT ON THE MAIN DRIVING AXLE. 155. Sometimes it happens that in designing small locomotives the eccentrics cannot be placed on the main axle, consequently we occasionally meet with a valve gear as shown in Fig. 205. In this valve gear the eccentrics are placed on the axle in front of the main axle. Placing the eccentrics on the front axle instead of the main axle will not change the previous rules we have given for designing the valve motion; but it should be noticed that, in order to preserve the lead, no matter in what position the link may be placed, as explained in Art. 151, the eccentric-rods are connected to the link in a manner which will put the lower end of the link in action when the engine is going ahead, or, in other words, the link must be raised when the engine is to run forward, and lowered when the engine is to run backward. Of course the eccentric-rods could be connected to the link so that it would be in the lower position when going ahead, and in the upper position when running backward that is, the link could be made to occupy a similar position to that in the link motions previ- ously illustrated, and for that matter would also work all right while in full-gear, but the lead will be destroyed when the link is placed in any of the intermediate positions for the same reasons as explained in Art. 151 ; and since we must have lead in whatever position the link is placed, we must suspend the link as shown in Fig. 205 MODERN LOCOMOTIVE COXSTRVCTIOX. It will also be found that in locating the lifting shaft according to the rules previously given, it will have to be placed in front of the link, instead of being placed in the ivur of it as has been found necessary in all the foregoing link motions. But by placing the lifting shaft, in the case now under consideration, in front of the link, we will gain an additional advantage, namely, in connecting the lifting-shaft arm to the reverse lever, the latter will be made to point ahead when the engine is going forward an important fact which should not be neglected or forgotten, because if the valve motion should happen to be arranged in a manner which would cause the reverse lever to point back while the engine is going ahead, the engineer may be thrown into con- fusion when, in an emergency, the engine has to be quickly reversed, and thus lead to accidents. CHAPTER IV. PISTONS. -CROSSHEADS. SLIDES. STUFFING BOXES. PISTONS. 156. Locomotive pistons consist of two principal parts, namely, the piston head and the packing. Locomotive pistons may also be divided into three classes, accord- ing to the construction of the head; the first class embracing all those in which the piston head is made up of more than one piece, such as shown in Figs. 206 and BED Fiff.20(i Fig.20? 207 ; this class of pistons we may call the " built-up piston." The second class will embrace the pistons in which the head is cast hollow, such as shown in Fig. 208 ; this class of piston we may call the hollow piston. To the third class belong the solid piston, such as is shown in Fig. 209. THE BUILT-UP PISTON. 157. Figs. 206 and 207. In this figure the piston head is made up of the following pieces : The spider, which is marked A ; the follower plate, or simply the follower, marked B ; and the follower bolts C, which unite the follower to the spider. In American locomotives the spider A is made of cast-iron. It should be made, in fact the whole piston should be made, as light as possible, and consequently its metal must be judiciously distributed, so as to obtain the required strength with the least amount of metal. By so doing, less counterbalance will be required, besides MODEK\ LOCOMOTirK COXSTRUCTION. 139 gaining other advantages. The spider is generally keyed to the piston-rod by the key /; sometimes the piston is secured to the rod by means of a nut, as shown in Fig. 208. In very large pistons, such as are used in stationary or marine engines, the depth of the spider (corresponding to the depth x in Fig. 206) is computed for strength ; the width of the packing (corresponding to the width y in Fig. 206) that is, the distance from the face of the flange of the spider to the face of the follower is generally made equal to . to ^ of the diameter of the piston ; the latter proportion being adopted for pistons of comparatively small diameter (as large as a locomotive piston 22 inches in diameter) and the former proportion for pistons of very large diameter. Consequently, in stationary engines, and also in marine engines, we often find pistons whose depth FiO.%08 Vifl.%09 at the center is greater than that at the circumference, so that when one face of these pistons is flat the other face will be part of a spherical surface. In locomotive pistons the depth x of the spider is determined by the key which holds it to the piston-rod. The dimensions of these keys, depth of spider, and size of piston- rods are given in Figs. 220 to 232. Now, practically, in locomotive pistons of small diameter the necessary depth x of spider does not give us an excessive depth for the packing, and in those of larger diameter the depth x will give a depth of packing agreeing with the proportions given for stationary and marine engines. Therefore the faces s and s.> of locomotive pistons are generally flat, sometimes slightly tapered towards the circumference, as shown in the figures. The follower plates (Figs. 206 and 207) are made of cast-iron, and usually cover the whole open end of the spider when follower bolts are used, as shown in the figure. FOLLOWER BOLTS. 158. In any mechanism having such a lii^li rate of reciprocating motion as a locomotive piston, bolts, unless carefully fitted, are liable to become loose and work 140 MODERN LOCOMOTIVE CONSTRUCTION. out. To prevent the follower bolts from becoming loose, they are extended into the spider through a distance which is at least equal to three times the diameter of the bolt, and great care is taken to make a good fit of the thread. Sometimes, on account of the rust, trouble is experienced when the follower bolts are to be taken out of the spider. To obviate this difficulty a few locomotive builders insert brass plugs into the spider. (See Fig. 210.) These plugs are tightly screwed into the spider and then riveted over at the ends. In these brass plugs holes are drilled and tapped to receive the follower bolts, preventing any rust from causing a difficulty in removing the bolts when it becomes necessary to do so. The construction of the hollow piston, shown in Fig. 208, needs no explanation, with the exception to state that a number of core holes B are cast in one side of the piston, and when the piston is cleaned the core holes are tapped and plugged up. The solid piston shown in Fig. 209 is used when extreme lightness is required. This form of piston is suitable for cast-iron, wrought-irou, or steel. PISTON PACKING. 159. A great amount of thought, labor, and expense has been expended in con- structing and perfecting a piston packing which shall give satisfaction under all circumstances, and consequently many different kinds of piston packing are in use. But we have noticed that the kind of piston packing which has given the best satisfac- tion so far is one in which two distinguishing features are found, namely, durability and simplicity ; and indeed these two features we should expect to find in any good piston packing, because any packing that will not remain steam tight for a consider- able length of time is troublesome, annoying, and unprofitable ; and a packing which does not possess the feature of simplicity is dangerous, particularly so in fast-running engines. The packing in the hollow piston, Fig. 208, consists simply of two cast-iron rings D 7), which are sprung into the grooves turned into the periphery of the piston. Each ring is cut in one place ; the favorite form of the cut is shown in Figs. 214 and 215. This piston, on account of its great simplicity, is a favorite one on many roads. It is more suitable for cylinders of large diameter than smaller ones, because in the latter there is danger of breaking the rings in attempting to spring them into the grooves. Similar packing rings are used for the solid piston shown in Fig. 209. In Figs. 206 and 207 we have represented another piston packing which, on account of its simplicity and durability, has in late years gained great favor among engineers, and is certainly an excellent piston packing for locomotives. It consists simply of two cast-iron rings D D, and one cast-iron T-ring marked E. We call this ring a " T-ring " because its cross-section resembles a T. The rings D D are cut open in one place, and consequently are called single-cut rings. Two ways of cutting these rings are generally adopted. Some master-mechanics will have the rings D D cut as shown in Fig. 213. Here a hole F F is first drilled and made oblong in the direction of F F, then through the center of the hole the ring is cut open square across. Care should be taken to cut out a sufficient amount of metal, so that when the packing ring is placed in the cylinder the two ends will not touch each other, but will leave an opening sufficiently great to allow for the expansion of the ring MOI>I-:I;\ tOCOJtOJtrK ro.v,sr/?rcrro,v. 141 when it becomes liot. The same remark applies to the hole F F; this should be made long enough, as shown, to allow a sufficient clearance around the pin which is inserted in this hole and driven into the T-ring, otherwise the expansion will force the ends of the packing ring against the pin and prevent the ring from acting as it should do. The object of this pin is to prevent the ring Z) from moving around the Fig.210 Fig.2'11 Fig.Zlit Fig.218 T-ring. When the rings D T) are cut in the manner just described, they are turned about i\ to , r ' (1 of an inch larger in diameter than the bore of the cylinder, so as to give the rings an inherent elasticity. The other way of cutting these rings is shown in Fig. 214. Here half the width of the ring is cut out through a distance of about 5 of an inch, which enables the ends of the ring to overlap each other about f of an inch. The writer believes (hut when a ring is to be- cut in this manner the best method to pursue will be as follows: First turn the ring large enough in diameter to allow for 142 MODERN LOCOMOTIVE CONSTRUCTION. the metal to be cut out. Then cut the openings A and B, Fig. 215, through half the width of the ring, and each about J of an inch long. When these are cut press the ends together, so that the ends will overlap each other about f of an inch ; through these reduced ends drive a small temporary pin, and then again turn the ring to fit the bore of the cylinder ; after that take out this pin, as it has served its purpose. Other pins are driven in the T-ring, which fit loosely in holes drilled in the packing rings, to prevent the latter from turning around the T-ring. As to the proportions of the cross-section of the rings D D (see Fig. 206), a differ- ence of opinion exists. Some master-mechanics make the width of the ring greater than the depth, others will insist on having the width smaller than the depth, but more frequently we find the cross-section to be a square. The writer believes that packing rings whose cross-section is inch square will give good satisfaction for cylinders 9 inches in diameter ; and this cross-section should be gradually increased for cylinders of larger diameter, in a manner which will bring the cross-section of the ring to f inch square for locomotive cylinders 22 inches in diameter. In the majority of locomotives the depth H of lings D D remains the same throughout, as shown in Fig. 216. They are made to press against the interior surface of the cylinder by their inherent elasticity, and when this elasticity is exhausted through constant wear, it can be partially restored by a few judicious light blows of the hammer in the inside of the ring. Since these rings will wear most at the opening, and in time wear the cylinders oval instead of cylindrical, it has been assumed that they have not a uniform pressure all around against the cylinder surface, and this is true. Hence, on account of this unequal pressure, some master- mechanics make these packing rings of the form as shown in Fig. 217, in which the depth H at the opening of the ring is less than the depth H opposite the opening. The object aimed at is, of course, to obtain as nearly as possible an equal pressure of the ring against the interior surface of the cylinder. But from the writer's experience, and upon careful inquiry, he is led to believe that rings of uniform depth throughout, as shown in Fig. 216, will give as good satisfaction as the ring shown in Fig. 217. Cast-iron is generally considered to be as good a metal as can be used for piston packing rings, as it wears well, particularly when the metal in the cylinder is hard, as it should be; furthermore, rings of the kind just described need but very little inspection, and can be used for a considerable length of time. 160. Sometimes the packing rings are cut into four or more pieces, and made to press against the interior cylinder surface by the aid of springs; the advantage claimed for this arrangement is an equal pressure against the cylinder surface. / DUNBAR PACKING. A notable packing of this kind is the Dunbar packing shown in Fig. 219A. The packing consists of two kinds of rings: one has an L-shaped cross-section and the other a square section. Each ring is cut into a number of sections in this case six in number and when put together the joints are staggered. These sections are pressed out by a number of springs made of round steel wire extending around the T-ring ; the latter is of the same form as is usually used for the ordinary class of pistons. But cut- XODERX LOCOMOTIVE COSSTRUCTION. 143 Fig. 219 A Platan for 10 In. Cylinder "Dunbar" ting the rings into so many pieces, and then introduc- ing springs, interferes with the simplicity of construc- tion, and therefore pack- ings of this kind have not been as frequently used in late years as formerly. T-RING. POSITION OF PACK- ING KINGS. 1 til. Fig. 206. The outer smi'ace of the T-ring is turned to fit easily the bore of the cylinder, so that when the T-ring becomes hot its expansion will not interfere with its free motion in the cylinder. The width of this ring must be turned to such dimensions that it can be held firmly in position by the follower plate, when the latter is screwed to the spider. The recesses turned at each corner of the ring will form the grooves for the packing rings when the piston is put together. Of course, the T-ring is not cut open. The advantage obtained by the use of this ring is that the packing rings can be readily placed in or taken out of the piston, without forcing the ends of the packing rings apart to place them into the grooves, as must be done when the solid piston is used. The packing rings must fit in the grooves very accurately, not too loose, yet free enough to allow the rings to adjust themselves to the interior surface of the cylinder. When both the packing rings are placed in position, their openings or cuts should not be in a straight line, but should be staggered, having a distance of 5 or 6 inches between them, as indicated by distance between the openings / /' in Fig. 206. It is always best to allow the openings of the rings to lie in the lower part of the cylinder ; but in no case should they be placed over a steam way. Tin- reason for this is that, since the rings are turned a little larger in diameter than the bore of the cylinder, they must be compressed in placing them into the cylinder ; and now, should the hold or grip upon them be lost through some accident or mishap while in the act of placing them in position, the ends of the rings may fly into the steam way, and generally in such cases they must be ruined by cutting them into several pieces, in order to take the rings out. BRASS PISTON PACKING. 162. Another very good packing for locomotive pistons is shown in Figs. 211 and 212. In former years this packing was the favorite, and even in late years some master-mechanics show a reluctance in giving it up, and consequently it is at present frequently met with. This packing consists of two brass packing rings /' /', one inside cast-iron ring M, the packing bolts K with nuts, and the packing springs L. The 144 -MODERN LOCOMOTIVE CONSTRUCTION. packing rings P P have grooves G G turned in them, and these grooves are filled with Babbitt metal. This metal will prevent the scratching of the interior of the cylinder surface, such as would be the case when brass alone is used. The rings P P are turned all over very accurately ; the width of each of these rings is equal to half the space between the flange of the spider and the follower plate, so that the rings will fill this space without binding, and have freedom to adjust themselves to the bore of the cylinder as the piston moves forward and backward. Consequently as will be seen by the illustrations, Figs. 220 to 232 the width of each packing ring for large pistons will be l inches, and for the smaller pistons In, inches. The depth of these rings is generally equal to f of their, width. Each ring P P is cut open in one place, usually at an angle as shown at F F, Fig. 211. The diameter of these packing rings should be sufficiently large to allow only for the amount of metal that is to be cut out of them, so that when the ring is placed in the cylinder the ends of the opening will be sufficiently apart to prevent the expansion from forcing the ends together. The cast-iron ring M is turned to fit the inside of the brass rings P P, is cut in one place square across, and its width must be exactly equal to the sum of the widths of the brass rings, so as to give it freedom to adjust itself to the inside of the brass rings. The thickness of the ring M is usually about % of an inch for large pistons, and about f% for smaller ones. The purpose of the ring M is to furnish a bearing for the springs L L, and to distribute their pressure equally on the packing rings; also to form a steam-tight joint with the interior of the brass rings P P. Dowel pins N, Fig. 212, are driven into the ring M and allowed to project into holes drilled into the brass rings P P, preventing the latter from moving around the ring M. The brass rings P P have but very little inherent elasticity, and consequently the packing springs L L are needed for the purpose of pressing the packing rings against the interior cylinder surface. In large locomotive pistons the springs L L are usually about 5 inches long, 2j inches wide, and of an inch thick in the center ; the thickness is reduced towards the ends. For smaller pistons these springs are about 4 inches long, 2 inches wide, and J of an inch thick. The packing bolts K K are generally f of an inch in diameter ; their heads, which are of the T form, are set into grooves cast into the hubs of the spider, which will prevent the bolts from turning when the nuts are screwed against the springs to press out and adjust the packing rings as may be required. PISTON-RODS. 163. Locomotive piston-rods, and, in fact, piston-rods for nearly all kinds of steam engines, are subjected alternately to a tensile and compressive stress. By tensile stress is meant that force which tends to produce fracture by pulling or tearing the piston-rod apart ; and by compressive stress is meant that force which tends to pro- duce fracture by crushing the rod. In calculating the strength of any piston-rod the tensile and also the oompressive stress to which it is subjected must be considered ; thus, for instance : We first find the diameter which will give the piston-rod sufficient MODESX LOCOMOTIVE CONSTRUCTION. 145 strength to resist the tensile stress; then we find the diameter which will give the piston-rod sufficient strength to resist the compressive stress. If we find that the diameter must be 3 inches to resist tensile stress, and only 3 inches to resist com- pressive stress, then the diameter of the rod must be made equal to 3 inches, otherwise there is danger of producing fracture by tearing; if, on the other hand, we find that the diameter of the piston-rod must be 3 inches to resist compressive stress, and only 2J inches to resist tensile stress, then the diameter of the piston-rod must be 3 inches, otherwise there is danger of buckling or producing fracture by crushing it. From these remarks we may conclude that in some cases the diameter of the piston-rod is determined and limited by the tensile stress, and in other cases by the compressive stress. Generally speaking, long rods that is, rods which are long in comparison with their diameters cannot resist as much compressive stress as tensile stress, consequently their diameters are determined by the former; short rods, on the other hand, cannot usually resist as much tensile stress as compressive stn-ss, hence the diameters of short rods are determined by the tensile stress. Loco- motive rods are comparatively short when compared with their diameters, and their ends are weakened by key ways or threads ; therefore the diameters are determined "by the tensile stress alone, and consequently in the following, compression will be left out of consideration. In speaking of the diameter of a piston-rod, we mean the diameter of that part of the rod which reaches from the piston to the crosshead. 164. When built-up pistons are used, the piston is keyed to the rod in the majority of cases ; occasionally we find the two united by a nut. The ends of the rod which fit in the piston and crosshead are made smaller in diameter than that of the rod, so as to form shoulders. The object of these shoulders is twofold: first, they will allow the rods to be re-turned when that becomes necessary through constant wear ; and secondly, it is considered to be good practice to have a shoulder against which the piston can be driven. The ends are tapered f of an inch in 4 inches that is, in 4 indies the diameter decreases of an inch. The end of the rod which fits in the piston must be made as short as the design will permit, so as to reduce the depth of the piston as much as possible. The crosshead end must be made a little longer than the piston end, because in the former the distance between the key and the shoulder of the piston-rod must be increased to obtain sufficient metal in the crosshead hub from the key to the end of the hub. The taper of the keys is \ of an inch in 12 inches. 165. Figs. 220 to 232 inclusive form an illustrated table of the pistons and rods from which all the principal dimensions can at once be obtained. In making this table the writer obtained the dimensions of rods and pistons used in modern locomo- tives and doing good work, but, as was to be expected, there was found to be no uniformity of proportions; but yet these proportions seemed to indicate that the tensile stress should not be greater than 10,000 pounds per square inch on the weakest part of the piston-rod. With this data and these proportions as a basis the writer formed this table, in which the dimensions have been obtained by calculation, so that when these dimensions are adopted and the pressure in the cylinder is 120 pounds, the tensile, stress per square inch on the weakest part of the piston-rod and key will not exceed 10,000 pounds. MHIIKRN LOCOMOTITE CONSTRUCTION. 147 Mostly all the dimensions given in these figures agree, and the others very nearly agree, with the sizes of pistons and rods used in first-class locomotives. The writer believes this table to be reliable. Locomotive piston-rods are made of iron, steel, and cold rolled iron. When cold rolled iron is used the piston-rods are not turned, the iron being rolled to the required size. In order to reduce the number of patterns as much as possible, it is customary to retain the same diameter for steel and iron piston-rods for a given diameter of cylinder ; that is to say, when a steel rod is to be used in place of an iron rod, the diameter of the former is made the same as that of the latter. Consequently, our remarks in regard to strength of locomotive piston-rods apply to iron as well as steel rods. But the reader must not be led to understand that there is no difference between the strength of steel and iron rods, and that in designing piston-rods for other engines the difference between the strength of steel and iron can be neglected. We simply wish to be understood that in locomotive practice only, the difference between the strength of steel and iron rods is left out of the calculation, so that the rod made of the weakest material will still be strong enough to do the work, and thus enable us to establish an interchangeability of wider range of the mechanism whose dimensions depend upon the diameter of the piston-rod, and also reduce the number of patterns. It is the general practice to allow on the piston-rod a tensile stress of 5,000 pounds per square inch, and not to exceed this. But it should also be remembered that new locomotive piston-rods are usually made of an inch larger in diameter than is necessary for the strength of the rod, so that in case the rod needs to be turned down on account of wear, it will still be strong enough to do the work. Conse- quently, after having found the correct diameter which the strength of the rod demands, we must increase this diameter by i of an inch, which will be the allowance for wear. Hence, when it is desirable to determine by calculation the diameter of a piston-rod suitable for a size of cylinder and a steam pressure not given in the table, the following rule may be employed : RULE 18. Multiply the area in square inches of the piston by the maximum steam pressure per square inch in the cylinder; the product will be the total pressure on the piston, and therefore the total tensile stress on the piston-rod. Divide this product by 5,000 ; the quotient will be the area in square inches of the cross-section of the piston-rod ; the corresponding diameter of this area, and an addition of J of an inch to this diameter, will be required diameter of the piston-rod. Putting this rule in the shape of a formula, we have : Area of the piston in square inches x pressure per square inch = area of the piston-rod, without allowance for wear ; then, diam. of area found + of an inch = required diameter of piston-rod. EXAMPLE 44. What should be the diameter of a piston-rod for a locomotive cylinder 18 inches in diameter ; steam pressure in cylinder, 120 pounds per square inch? 1254.47 x 120 "000 ~ ~ ^ ' area * piston-rod, without allowance tor wear. 148 MODERN LOCOMOTIVE CONSTRICTION. Diameter of an area of 6.1 square inches = 2yf inches, nearly. 2H + 4 = 2-J-f inches = required diameter of piston-rod. In Fig. 229 we find this diameter to be 3 inches. There are in this table several diameters which will slightly exceed the diameters found by this rule. The reason of this is that in making this table the writer has followed the general practice of locomo- tive builders, namely, avoiding -^ of an inch in the diameters of the piston-rods ; also making the increase of the diameters of rods for the different sizes of cylinders as gradual as possible. The piston-rod in Fig. 232 is about of an inch less in diameter than would be obtained by calculation. We have given this small diameter because such was used in the few engines of this size that we have met. The figures obtained by the rule will give sufficient strength to the piston-rods ; the figures in table agree closer with practice. It will be well to remark here that the area of the weakest part of the piston-rod is practically equal to one-half the area of the cross- section of the rod; and this remark applies equally well to the piston-rods which are keyed to the piston, and those which are united to it by a nut. Thus, for instance: Let Fig. 233 repre- sent one end of the piston-rod ; then the section through a b will obviously be the weakest part of the rod to resist tensile stress ; and it will generally be found that the area of this section is equal to one-half the area of the section through c d. Or, again, when the piston-rod is united to the piston by a nut (such a rod is repre- sented in Fig. 219), then the area of a section through the bottom of the thread, which is the weakest part, will be equal to about one- half the area of the rod. Consequently it follows that, by allow- ing 5,000 pounds per square inch of section at c d, Fig. 233, the ten- sile stress cannot exceed 10,000 pounds per square inch at a b, which is correct, and agrees with practice. In calculating the strength of the key, we may assume, and do so without fear of error, that the tensile stress is equal to the shearing stress. The key is subjected to a double shear; that is, shearing must take place at two places before fracture can occur. Hence, the area of one cross-section of the key must be equal to one-half the area at a & in Fig. 233. TABLE 14. -7; Fig. 233 Diameter of Piston. Diameter of Piston-rod. Large Diameter of Tapered End. 9 inches. 1^ inches. H inches. 10 U 1* 11 2 If 12 3* H 13 2 o 14 2| 2i 15 2* 16 2* 3* 17 2J 21 18 3 2J 19 3* 20 3 3 22 3f 3J LOCOMOTIVE CONSTRUCTION. 149 The dimensions in the foregoing table agree with those given in the illustrations. The principal dimensions of pistons are given in Figs. 220 to 232. CROSSHEADS. 106. The function of a crosshead is to form a connection between the piston-rod and the connecting-rod, making the piston-rod move in its true course, in a straight line, while the connecting-rod moves through various oblique positions. Consequently we may say the crosshead consists essentially of a socket, to which the piston is keyed ; a journal, on which one end of the connecting-rod works ; and lastly, sliding surfaces, which are compelled to remain in contact with the guides, and thus guiding front end. (I Fig. 236 MISSION SUITABLE FOR CAST IRON. Cylinder It'diumeter * gjf'ctrofce. the end nf the pisloii-n>d in its true course, preventing the thrust of the connecting- rod from bending or injuring the former. It will hardly seem necessary to give names to such familiar mechanism as here represented ; but since the different pieces are not named alike by all mechanics, the writer deems it advisable to name the pieces, so as to avoid misunderstanding here- after. Similar letters in the different views represent the same piece. Figs. 234, 235, and 236. S represents the guides, frequently called slides (some mechanics call these the slide-bars or guide- bars ; we shall simply name these the guides or slides) ; Z?, the guide-blocks ; c, the crosshead ; ?, the crosshead wings, or simply the wings (in some books these are called slides or slide-blocks) ; <7, the gibs ; P, the crosshead pin ; k, the crosshead key ; and y, Fig. 2J5 the guide-yoke. In locomotive construction three styles of i-msslieads are used, and these we may classify as follows : 150 MODERN LOCOMOTIVE CONSTRUCTION. First, crossheads which require four guides; second, crossheads which require two guides ; third, crossheads which require one guide. 167. Fig. 234 represents a side view, Fig. 235 an end view, and Fig. 236 a plan of a crosshead and guides. This crosshead, as will be seen, requires four guides. This style of crosshead is generally used (not always) in eight-wheeled locomotives such as shown in Fig. 1, and ten-wheeled locomotives as shown in Fig. 3. When a crosshead is to be designed for one of these engines, we must keep in mind the following con- ditions. In the eight-wheeled and ten-wheeled locomotives the rear truck wheels are situated directly behind the cylinder saddle and between the guides and the frames, and these wheels must have a sufficient space for the lateral play when the engine is running over a curve. Now this space is limited by the position of the cylinders. Thus, for instance, the centers of the cylinders are always placed as close to the frames as possible, which, of course, will limit the space between the guides and frames and often give an insufficient space for the lateral play of the rear truck wheels. But, since it is always of great importance to keep the centers of cylinders as close to the frames as can be done, we should not attempt to spread the cylinders so as to obtain sufficient space for the wheels until allot her resources fail. Now let us consider the distance between the center of the cylinders and the top of the track, and see if by some means sufficient room can be obtained for the wheels to pass under- neath the guides and thus gain for them a sufficient space for their lateral play. In the first place, the centers of cylinders are usually placed from 1 to 2 inches above the centers of di'iving wheels when the engine is in the ordinary good running condition. The center of the crosshead pin P must, of course, remain in line with the center of the piston-rod, or what amounts to the same thing the center line of the cylinder ; hence the height above the track to the center of the cylinder or the crosshead pin P will also to a great extent limit the space we wish to obtain. Now, only one more resource remains by which we may obtain the desired space, and that is, raising the guides above the center of the crosshead pin P. If this fails to give us sufficient space, then we must either spread the centers of the cylinders, or adopt a crosshead such as is shown in Fig. 241, or do both. Usually it is'fouud that a crosshead with the guides raised above the center of pin P, as shown in Fig. 234, will answer the purpose and still allow the center of the cylinders to remain as close to the frames as they can possibly be placed. This arrangement will enable the truck wheels to pass under- neath the guides as far as will be necessary. Here the flanges have not entered into our consideration, and indeed it is not necessary that they should, as there will always be, in this class of engines, sufficient space between the frames and guides for the lateral play of the flanges. Sometimes in narrow-gauge engines the side of the frames must be cut in order to clear the truck wheel. It must also be remarked that the engine and truck springs, particularly the latter, will cause the cylinders and guides to move up and down, and since the wheels have not this movement, a sufficient clearance between the under side of the guides and top of truck wheels must be allowed, to prevent the guides from striking the top of truck wheels when the springs impart a vertical movement to the guides. This style of crosshead, Fig. 234, is usually made of cast-iron, sometimes of MODERN LOCOMOTITE COXSTBl'CTION. 151 malleable iron. The crosshead pin P and the crosshead are cast in one piece. The pin /' is generally finished off by hand, sometimes with special machinery. In order to take up quickly and readily any wear between the guides and the wings of the crosshead, the brass gibs g are introduced. The lips at the ends of these gibs prevent them from moving endways, and the lugs h cast to the gibs and fitting in the slots cut in the wings of the crosshead will prevent the gibs from slipping out sideways. When the wear is to be taken up, thin copper liners are inserted between the gibs and the wing. 168. Some master-mechanics prefer crossheads with brass gibs, because, the brass being softer than the iron, they believe that there is not so great a liability to cut the guides as when cast-iron bears directly against them, which will be the case when crossheads without the gibs are used. Cutting the guides is always a serious matter, Q. Q. D- S r P= ^ ;=> Q. 0- D Fip. 252 mg. 254, Fig. 253 and if cutting does occur, it is always preferable that the gibs should be cut or ruined, rather than the guides, as the former are cheaper to replace, and can be replaced in less time (another important matter in railroading) than ruined guides. Yet experience also teaches that when guides are properly case hardened, and crossheads without gibs are used, so that cast-iron bears directly against the guides, cutting of the guides is prevented by running a new engine at first slowly and carefully, allowing the cast- iron wings to wear down to smooth, hard surfaces ; after that there is little danger of cutting the guides, providing they are kept oiled. Consequently we meet with many locomotives in which the crossheads have no brass gibs and give perfect satisfaction. Crossheads without gibs have the wings babbitted, as shown at a a a in Fig. 252. Three or more rectangular recesses, about or f of an inch deep, f of an inch wide, and as long as the width of the wing will allow, are cast in the wing, and then filled with Babbitt metal. Sometimes as many recesses, \ or f of an inch deep, Ij inches in diameter, as there is room for, arranged in a manner as shown at b b b in Fig. 253, are bored in the wing, and then filled with Babbitt metal. A few years ago these recesses were sometimes filled with glass disks. When these were used, the bottom diameter of the recess was larger than the upper diameter, and also the lower diameter of the glass disk larger than the upper one. This disk was then placed in the recess, and Babbitt metal poured around it, as shown in Fig. 254, and thus held firmly in the recess. 169. Objections are sometimes raised against crossheads with the pins P cast in one piece, as it is difficult to true up these pins when necessary, and therefore cross- heads similar to that as represented in Figs. 237, 238, 239, and 240 are sometimes preferred. 152 MOI>KI;\ LOCOMOTIVE <:o.\xTi;r<"n<>\. This crosshead consists of several pieces. Fig. 240, His a wrought-iron hub with fork end. This hub is keyed to the piston-rod. The wings w 3 w 3 , with flanges 1 3 1 3 , are made of cast-iron. The bushing F is made of wrought-iron case hardened, the grain of the iron running around the bushing, and not in the direction of its length ; the fork end of the hub H is bored out large enough to receive the bushing. The bolt 3 is made of wrought-iron not case hardened ; the outer plate 3 is made of brass and LOCOMOTIVE CROSSHEAD 't n Cylinders 17 diatn. 84 stroke. 6 iJS * ., * Cylinders If diam. 34 stroke. the inner plate b 3 of cast-iron. The purpose of the holes r 3 r 3 in the wing is to reduce the weight of the latter. Thin brass plates d d (Fig. 239) are riveted to the bearing surfaces of the wing, as shown. In putting this crosshead together, the bolt o 3 (Fig. 240) is passed through the cast-iron plate 1 3 , and through the wings, with the hub H and bushing F between them. In screwing these together, the wings w 3 w 3 bear hard against the ends of the bushing F, and thus prevent the closing up of the fork on the hub H. The brass plate a 3 is then fastened to the outer wing by two f screw bolts, covering up the nut of the bolt o 3 and giving a nice and clean outer appearance to the crosshead. The f screw bolt n 3 prevents the cast-iron plate from turning on the bolt o 3 . The bushing F forms the crosshead pin, and when it becomes worn, can easily be removed and replaced. This design makes a very good crosshead, but on account of its expense is not often used. When crossheads of this kind or those without gibs are used, thin copper strips are inserted between the guide-blocks B B and the guides s s at the time the engine is being built. Then when it becomes necessary to take up the wear between MODEKX LOCOMOTIVE CONSTRUCTION. 153 the guides and the crosshead, these copper slips are one by one removed, thereby bringing the guides together. 170. The pressure of locomotive crossheads against the guides caused by the thrust of the connecting-rod should not exceed 50 pounds per square inch ; and how to find this thrust we will presently explain. From this remark we conclude that the sliding surfaces of the wings of crossheads. shown in Figs. 234 and 237 must contain a certain number of square inches, and consequently if the width of the guides is increased the length of the wings is made less, and when the length of the wings is shortened the guides are also shortened, which is always desirable. When four guides are employed, as shown in Figs. 234 and 237, we naturally obtain a wide sliding surface, and consequently the crossheads and guides shown in these figures are comparatively short ; the guides, being placed well up above the rails, are kept comparatively free from dust ; the crosshead is light ; in fact, the whole arrangement is well adapted for eight-wheeled passenger engines, or engines having a four-wheeled truck in front. The vertical distance between the guides, as shown in Figs. 234 and 237, should be only sufficient to admit a wing of a minimum depth. In these figures it will also be noticed that the crosshead pin P is, horizontally, somewhat out of the center of the wings or sliding surfaces of the crosshead. The reason for this is that designers will always endeavor to make the crosshead, and consequently the guides, as short as possible. Now, because the required strength of the crosshead will fix the distance between the center of the pin P and the front end of hub, this distance is limited, but by moving the wings a little ahead of the pin P, which can often be done, the distance from the front of the hub to the rear end of the wing is somewhat decreased, and therefore the guides can also be made a little shorter. But in the writer's opinion such practice should be avoided as much as possible, and the pin P should be kept central with the wings or sliding surfaces of ah 1 crossheads ; by so doing the latter will wear more evenly. 171. The type of crosshead of which a side elevation is shown in Fig. 241, an end elevation in Fig. 242, and a plan in Fig. 243, is occasionally used for eight-wheeled passenger engines, but the writer believes that this crosshead is better adapted for a mogul engine, such as is shown in Fig. 2, and a consolidation engine, such as is shown in Fig. 4, and for these engines it is very often used. This design of crosshead is suitable for cast-iron, of which these crossheads are made, and the dimensions here given are suitable for a cylinder 20 inches in diameter. The crosshead pin P is either made of steel or wrought-iron case hardened. The head of the pin is always placed towards the driving wheels ; by so doing as will be obvious the cylinders can be brought closer together and still leave room enough for the crosshead to pass the crank-pin of the front driving wheels. The side of the crosshead in which the head of the pin P is inserted we shall lien-after call the inner side of the crosshead, and the opposite one the outer side. In the majority of crossheads of this type brass gibs <1i'.l-i (Fig- 242) are used. In order to take these out quickly when necessary, or to put in liners when the wear demands it, the outer flanges f 2 f 2 are bolted to the cross- head ; the inner flanges are cast to it. These flanges and the lips cast on the ends of the gibs will prevent the hitter from slipping out of place. In designing a crosshead one, great object aimed at is to make it as light as possible, and still leave it sti-ong enough 154 MODERN LOCOMOTIVE CONSTRUCTION. -Ifc DESIGN SUITABLE FOR CAST IRON DESIGN SUITABLE FOR WROUGHT IRON OR CAST STEEL. Cylinder O inches diameter. 34 Inches stroke. MODERN LOCOMOTIVE CONSTRUCTION. 155 to meet any emergency ; consequently the distance between the guides must be as short as possible. This distance is determined by the oblique positions of the connecting- rod. The method employed for finding the distance between the guides will be explained hereafter. Some master-mechanics raise an objection to this type of cross- head, because when it is used in engines which have driving wheels of comparatively small diameter, as is the case in freight engines, the guides are brought too close to the rails and consequently exposed to the dust, which will wear the guides and cross- Ix-tid too fast. To avoid this difficulty, crossheads are used of which Fig. 244 is a side elevation, Fig. 246 an end elevation, Fig. 247 a plan, and Fig. 245 a view of the cross- head pin P. This design of crosshead is adapted for wrought-iron or cast steel, and is made of either one or the other material. The dimensions here given are suitable for cylinders 20 inches in diameter with a maximum steam pressure of 120 pounds per square inch. Some types of wrought-iron crossheads are very expensive to make, and if wrought-iron is insisted upon, then this design recommends itself, as the expense connected with making a crosshead of this type is comparatively small. Referring to Figs. 244 and 246 it will be seen that this crosshead consists simply of a hub H H 2 , to which the piston-rod is keyed. To this hub are forged two deep flanges F F 2 . These flanges extend upwards and terminate a little below the upper guides S S 2 . Between these flanges a cast-iron block h h 2 is bolted by a number of bolts of an inch in diameter ; these bolts extend through the flanges and the cast-iron block. To the upper and lower faces of the block Ji h 2 the brass gibs g g 2 g 2 are fitted. The gibs are held in position sideways by the flanges F 2 F 2 , and endways by the lips cast to the gibs ; for additional safety two pins r r one inch in diameter are driven through the gibs g g and the block h. The flanges of the upper gib g. 2 slide along the sides of the upper guide, and the flanges F 2 F 2 slide along the sides of the lower guides, thus forming good deep sliding surfaces which will guide the end of the piston-rod in a straight line laterally, although not with such steadiness as the crosshead shown in Fig. 241 will do ; and in this respect the crosshead represented in Fig. 244 is somewhat inferior to the one shown in Fig. 241. The gibs in the crosshead shown in Fig. 244 are not so readily removed as in those shown previously, because in the case before us, in order to take out the gibs the upper guide must be taken off, besides taking out all the bolts which hold the block 7i, and this is not always an easy matter. The distance from the center of the crosshead pin P to the lower surface of the bottom guide must be as short as possible ; it should be only sufficient to allow the connecting-rod when in an oblique position to clear the edge o of the lower guide. 172. Fig. 248 is a side elevation, Fig. 250 an end elevation, and Fig. 251 a plan of another crosshead and guide ; and Fig. 249 shows the crosshead pin P. This crosshead is made of cast-iron, and, as will be seen, requires only one guide. This design of crosshead should only be used for small locomotives ; the dimensions here given are suitable for a cylinder 15 inches in diameter, and indeed this crosshead is seldom used on engines having cylinders larger than 15 inches in diameter. This crosshead, with the exception of the plate F F 2 which is bolted on, is cast in one piece; this arrangement allows the brass gibs to be readily placed in position, and quickly removed when necessary. The distance between the guide and the pin P must be such as will allow the end of the guide to clear the connecting-rod 156 MODERN LOCOMOTIVE CONSTRUCTION. when in an oblique position. The writer believes this crosshead to be inferior to all the others shown, because in his opinion it will not guide the end of the piston-rod laterally as steadily as the others. Yet it is a very cheap crosshead, and seems to work well in small engines. TO FIND THE THRUST OF THE CONNECTING-ROD. 173. When the connecting-rod stands in an oblique position, for instance such as will occur when the crank is at half stroke, the connecting-rod will force the crosshead Fig. 250 Fig. 249 Inner side, Fig. 251 DESIGN SUITABLE FOR CAST IKON. Cylinder IS incites diameter. SO inches stroke. against the guides ; and this force which presses the crosshead against the guides is called the thrust of the connecting-rod. The amount of this thrust, or the magnitude of this force, can be found by two methods : The graphic method, and by calculation. We will first explain how this thrust can be found by the graphic method. MODERN LOCOMOTIVE CONSTRUCTION. 157 Fig. 252A. Let D be the center of the driving axle, C the center of the crank-pin, P the center of the crosshead pin, S S the guides, D I the center line of motion, and the circumference R C the path of the center of crank-pin. We shall assume that steam follows the full stroke of piston. It is required to find the thrust of the con- necting-rod, or the pressure of the crosshead against the guides. The total steam pressure on the piston is transmitted through the piston-rod to the crosshead pin P, and from thence it is transmitted through the connecting-rod to the crank-pin C. The directions in which this steam pressure acts is in the direction of the center line of the piston-rod, and in the direction of the center line of the con- necting-rod. At the beginning of a stroke, the center line of the piston-rod and the center line of the connecting-rod will lie in one and the same straight line, and therefore we assume that in this position there will be no thrust, or, in other words, the steam pressure will not cause any pressure between the crosshead and the guides. When the crank stands perpendicular to the center line of motion I) b, we may assume that for the purpose of finding the thrust the angle formed by the line D b and the center line C P of the connecting-rod will be the greatest, and therefore we conclude that in this position the thrust of the connecting-rod will also be the greatest. It is now our object to find the intensity of the thrust, or the magnitude of this force, when the crank D C stands at right angles to the center line of motion D b. Draw the center line of motion D b ; on this line take any point, as D, to repre- sent the center of the driving axle ; through the point D draw a line D C perpendicu- lar to the line D b, and make D C equal to the length of the crank. From C as a center, and with a radius equal to the length of the connecting-rod, draw a short arc cutting the line D b at the point P ; this point will be the center of the crosshead pin, and the line C P will represent the center line of the connecting-rod. Prolong the line C P to e, making P e equal to C P. Through the point P draw a line P a perpendicular to the line D b ; through the point e draw a line e b parallel to P a, and again through the point e draw a line e a parallel to P ft ; then P a e b will be a parallelogram, which is called the parallelogram of forces. Now in mechanics, which is that branch of science which treats of the effects of forces upon matter, it is shown that forces can be completely represented by straight lines, or, in other words, the magnitude of a force and the direction in which it acts can be represented by a straight line. It is also further shown that in a parallelogram of forces, such as we have just completed, the magnitudes of the forces are pro- poi-tional to the lengths of the sides of the parallelogram of forces ; that is to say, if the length of the side P a in our parallelogram is equal to the length of the side P b, then the force represented by the side P a will be one half, of the force represented by the side P b ; or again, if the length of the line P a is equal to of the length of P fc, then the force represented by the line P a will be one quarter of the force represented by the line or side P b. Here, then, it may be said that we have a point P which is held in equilibrium by three forces. The magnitude of these forces and the direction in which they act are completely represented by the length and the direction of the three straight lines C P, P b, and P a. The line P b represents the total steam pressure on the piston, which is 158 MODERN LOCOMOTIVE CONSTRUCTION. acting in the direction of the center line of the piston-rod ; the line C P represents a force acting in the direction of the center line of the connecting-rod ; and the line P a represents a force acting in a direction perpendicular to the guides, and is the thrust of the connecting-rod, or, in other words, the line P a represents the magnitude of the force which presses the crosshead against the guides, and which, according to our problem, was to be found. 174. In order to find the force or thrust P a it is not necessary to draw the cross- head, guides, piston-rod, and as many lines as we have done in this figure (this was simply done to make the principles plain), but we can, without adding any new principles or changing the foregoing ones, obtain the same forces by constructing the triangle, Fig. 253 A, which may be drawn full size, half size, or to any convenient scale thus: Draw any straight line P b (Fig. 253A) ; on this line take any point, as 6, and through this point draw a line b e perpendicular to the line P I ; on the line b e lay off a point e ; the distance between the points b and e must be equal to the length of the crank. From the point e as & center, and with a f Fig.ZBZA * r 7 radius equal to the length of the connecting-rod, describe a short arc cutting the line P b in point P ; join the points P and e by a straight line, and complete the triangle P b e. Now, if the dimensions of engine and steam pressure in Fig. 253A remain the same as those in Fig. 252A, the triangle shown in Fig. 253A will be equal to any of the triangles as P b e, P a e, and P D C in Fig. 252A, and consequently the sides of the triangle in Fig. 253A will repre- sent the same forces as the sides P a, a e, and the diagonal P e of the parallelogram P a b e in Fig. 252A. PRACTICAL APPLICATIONS OF THE FOREGOING PRINCIPLES. 175. EXAMPLE 45. Diameter of the piston is 16 inches, the stroke is 24 inches, length of connecting-rod 84 inches, and the steam pressure is 120 pounds per square inch ; steam follows full stroke : find the thrust of the connecting-rod or the pressure of the crosshead against the guides. Draw the line P b (Fig. 253A) ; at any point b on this line erect the perpendicular b e ; make the length of e b equal to 12 inches (which is the length of the crank or half the given stroke). From e as a center, and with a radius equal to 84 inches (the given length of connecting-rod), describe a short arc cutting the line P b at the point P ; join P and e by a straight line, and the triangle will be completed. The total steam pressure on the piston is found by multiplying its area in square inches by the steam pressure per square inch, and this total pressure will be equal to 24,120 pounds (the fraction has been omitted) ; hence the length of the line P b will represent 24,120 pounds. Now assume that we have a narrow strip of paper whose length is exactly equal to the length of the line P b, and that this paper is divided lengthwise into 24,120 equal parts, then each division will represent one pound ; laying this piece of paper (or scale, as we may call it) on the line e b, we find that this line will contain 3,481 MODERN LOCOMOTirE CONSTRUCTION. (iiciirly) <>t' the number of divisions on the paper; hence we conclude that the thrust, or the pressure of the crosshead against the guides, is 3,481 pounds. But to divide the line P b into 24,120 equal parts would require too much time and labor, hence the following method is used : Let us adopt 4 of an inch to represent 1,000 pounds; then since 24,120 pounds is represented by line P ft, we lay off from the point P on the line P b twenty-four J inches, which will then represent 24,000 pounds, because each inch represents 1,000 pounds. In order to represent the remaining 120 pounds, which are very nearly equal to of 1,000 pounds, we must add & of inch (which is equal to -^ of an inch) to the twenty-four % inches ; or, in short, from the point P on the line P b lay off a point x ; the distance between the points P and x must be equal to 12-^ inches. Through the point x draw a line x y perpendicular to the line P b and cutting the line P e in the point y ; then the line x y will represent the thrust of the connecting-rod, and since the length of this line is very nearly equal to If inches, which we obtain by measure- ment, and since each inch represents 1,000 pounds, we know that the pressure of the crosshead against the guide is not quite but very nearly equal to 3,500 pounds ; and this answer is in most cases near enough for practical purposes. But should it be necessary to find the amount of this thrust accurately, then the simplest way to determine it is by calculation ; and if the foregoing graphic method is understood, then there should not be any difficulty in understanding the following calculations, which are based on the principles already introduced in connection with the graphic method, thus : 176. We have already seen that the magnitudes of the three forces which hold the point P in Fig. 252A in equilibrium are represented by the three sides of the triangle shown in Fig. 253A. Now we know the length of the line P e, which, according to our example, is 84 inches ; we also know the length of the line b e, which is 12 inches, but the length of the line P b we do not know, yet we do know that the length of this latter line must represent 24,120 pounds. If we now find by calculation (instead of construction as before) the length of the line P ft, then, since we know the lengths of the other lines or sides of the triangle we shall have no difficulty in computing the number of pounds that each of the sides of this triangle represents, because the magnitudes of the forces are proportional to the length of the lines. The triangle P e b is by construction a right-angled triangle, and consequently to find the length of the side P b we subtract the square of the side b e from the square of the side P e ; the square root of the remainder will be the length of the side P b. The length of P e is 84 inches, the length of b e is 12 inches. The square of 84 is equal to 84 x 84 = 7,056, and the square of 12 is equal to 12 x 12 = 144, and 7,056 - 144 = 6,912. The square root of 6,912 is equal to 83.13+ inches, which is the length of the side P b. But the side P b and consequently the 83.13 inches represent 24,120 pounds ; therefore the number of pounds of the force represented by the side b e, which bears the same proportion to 24,120 pounds as the length of b e bears to P b, is found by the simple rule of proportion, thus : 83.13 inches : 12 indies :: 24,120 : the answer; hence, 24,120 x 12 ., 1U1 go -.o ^MHI pounds, 160 MODERN LOCOMOTIVE CONSTRUCTION. Therefore the magnitude of the force represented by the side b c is equal to 3,481 pounds, which is the pressure of the crosshead against the guides. Now putting the whole foregoing calculations in the shape of a formula, we have the following : FORMULA AND KULE FOR FINDING THE THRUST OF THE CONNECTING-ROD BY CALCULATION. Length of crank in inches Total pressure of steam on piston x ^ (length of CO nneeting-rod in inches) 2 - (tentfh~of"^Snk"in inches) 1 = thrust of connecting-rod. Or, in ordinary language, we have the following : RULE 19. Multiply the total steam pressure in pounds on the piston by the length of the crank in inches, and call this product a ; then from the square of the length of the connecting-rod in inches subtract the square of the length of the crank in inches, and find the square root of the remainder ; divide the product a by the last answer, the quotient will be the thrust of the connecting-rod in pounds. 177. The foregoing rule will give the thrust of the connecting-rod correctly in stationary and marine engines, or in all engines in which the center I) of the crank- shaft (Fig. 252A) cannot move out of the center line of motion D b ; but such conditions do not exist in locomotives, hence the foregoing rule must be somewhat modified, so that it will apply to them. Fig. 254A. Let D b represent the center line of motion ; I), the center of driving *'(/. 254 A axle ; C, the center of crank-pin ; the circumference E C, the path of the center of crank- pin ; and P, the center of the crosshead-pin. In locomotives the driving-axle box can move up and down in the pedestals, and consequently the center 7), and with it the path E C of the center of crank-pin, will move out of the center line of motion D b. In order to obtain the greatest thrust of a connecting-rod in a locomotive, we find the extreme lower and upper position C* 2 and C 3 of the crank-pin when the center line D <7 2 of the crank stands perpendicular to the center line of motion D b. Now let C 2 represent the center of crank-pin in its extreme lower position; then in order to construct the parallelogram of forces we proceed in a manner similar to that adopted before, namely: From the point 6' 2 as a center, and with the length of the connecting-rod as a radius, describe a short arc cutting the center line of motion D b at the point P, which MODERN LOCOMOTIVE CONSTRUCTION. will be the position of the center of crosshead-pin when the crank stands at right angles to the center line of motion and the crank-pin in its extreme lowest position. From C., and through P draw a straight line, and produce it towards e ; make the line P e equal in length to that of C 2 P, or, in other words, to the length of the connecting- rod. Through the point e draw a straight line e a parallel to P 6, and through the points /' and e draw the lines P a and b e perpendicular to P b, thus completing the parallelogram of forces P a b e. Now, if in Fig. 254A the length of the connecting-rod, crank, and the total steam pressure is the same as those in Fig. 232A, the line b e in Fig. 254A must be considerably longer than b e in Fig. 252A, and therefore the thrust represented by the line b e in the former figure must be greater than the thrust in the latter figure. Consequently the formula for determining the thrust of a locomotive connecting-rod will be as follows : BULE 20, IN SYMBOLS. TO FIND THE THRUST OF A LOCOMOTIVE CONNECTING-ROD. Let P represent the total pressure of the steam in pounds on the piston ; L, the length in inches of a line drawn perpendicular to the center line of motion D b and measured from the line D b to the extreme lowest position of the center C of the crank-pin ; K, the length of the connecting-rod in inches ; T, the thrust of the connect- ing-rod, or the pressure of the crosshead against the guides in pounds. Then P x = L = = T. V K* - L* If the line D C 3 should be greater than D C 2 , then the thrust will be the greatest when the crank-pin is in its extreme upper position, and in the calculation the length of D C y should be taken in place of D C 2 . APPROXIMATE RULE FOE FINDING THE THRUST OF A CONNECTING-ROD. 178. When the length of the connecting-rod is very great in comparison with that of the crank, then the difference between the lines P e and P b is very slight, and for many practical purposes this difference may be neglected. In such cases we assume that the length of the line P e will represent the total pressure on the piston, and consequently the rule for finding the thrust becomes very simple. APPROXIMATE RULE 21. Divide the length of the crank in inches by the length of the connecting-rod, and multiply the quotient by the total steam pressure on the piston ; the product will be the thrust of the connecting-rod against the guides, in pounds. Applying this rule to Example 45, we have the following result : It will be remembered that the total steain pressure on the piston was found to be equal to 24,120 pounds, the length of the connecting-rod is 84 inches, and the length of the crank, 12 inches. Hence if x 24,120 = 3,445.71+ pounds = thrust of the connecting-rod. The thrust of the connecting-rod found by Rule 1 ( J was 3,481 pounds. The dif- 162 MODERN LOCOMOTIVE CONSTRUCTION. ference between the two answers is so slight that it may be neglected, and in cases of this kind the simplest rule can be used. 179. lu Fig. 255 we have shown the method of finding the thrust of the connect- ing-rod for any other position of the crank. Let D P represent the center line of motion ; D, the center of driving axle ; C, the center of crank-pin ; D C, the position of the center line of crank ; and the circumference R C, the path of the center C. Now, in order to find the thrust of the connecting-rod when the crank-pin is in this position, Fig. 355 we draw through the center C a line A C, perpendicular to the center line of motion D P. And from C as a center, and with a radius equal to the length of the connect- ing-rod, describe a short arc cutting the line D P at the point P ; join C and P by a straight line, thus completing the triangle A C P, shown in heavy lines for distinction. The line A P will again represent the total steam pressure on the piston, and the line A C the thrust, or the pressure of the crosshead against the guide. To find the magnitude of the force represented by the line A C, we have the following approxi- mate rule : RULE 22. Divide the length of the line A C in inches (that is, the perpendicular distance from the center of the crank-pin to the center line of motion) by the length of the connecting-rod in inches, and multiply the quotient by the total pressure of steam on the piston ; the product will be the thrust in pounds. Thus: EXAMPLE 46. If the total pressure is 24,120 pounds, the length of the connecting-rod is 84 inches, and the length of the line A C is equal to 8 inches (by measurement), what will be the thrust of the connecting-rod ? / T x 24,120 = 2,287 pounds = pressure of the crosshead against the guides, or thrust of the connecting-rod. Should it be desirable to obtain this thrust more accurately, then apply Rule 19, and instead of using the length of the crank as stated in that rule, use the length of the line A C in Fig. 255 ; the length of the line A C is always found by measurement. Remember that in all these examples the steam follows full stroke. 180. In passenger locomotives, or other locomotives in which the crank generally turns in the same direction, the upper crosshead gibs will wear faster than the lower gibs. This is explained in the following manner : Let the arrow 2 in Fig. 254A represent the direction in which the crank turns when the locomotive is running in a forward direction ; then when the crank-pin is at C 2 the reaction of the connecting-rod will be in the direction of the arrow 3, causing the crosshead to be forced against the upper guide, as indicated by arrow 5 ; when the crank-pin is at (7 3 the reaction of the connecting-rod will be in the direction of arrow 4, and again force the crosshead against the guides, as indicated by arrow 5 as before. MODEIty LOCOMOTIVE COXSTRUCTWX. 163 In fact, throughout the stroke when the engine is going ahead, the erosshead will press against the upper guide; but it should be remembered that, when the center line of crank stands perpendicular to the center line of motion, then the pressure of the crosshcud against the guides will be the greatest; or, we should say, that in the neigh- borhood of the center of the guides the pressure will be the greatest, and will gradually decrease as the crosshead approaches the ends of the guides. In switching engines which are run as often backward as forward, the upper and lower gibs of the cross- head will wear very nearly alike, because in running forward the pressure of the erosshead is against the upper guides, and in running backward the pressure is against the lower guides. PROPORTIONS OF CROSSHEAD. 181. The sliding surfaces of a erosshead should not be too large, as this will make the erosshead too heavy ; neither should they be too small, because with small sliding surface the pressure per square inch on these surfaces will be increased to an extent which will heat the guides and cause abrasion or cutting. Now it will be apparent that before we can determine the dimensions of the sliding surfaces, we must know the pressure which can be allowed per square inch on these surfaces for the best practical results. Knowing this pressure, and also the total pressure of the cross- head against the guides, which must be provided for, the calculations for obtaining the dimension of the sliding surfaces or the length and breadth of the gibs will be an easy matter. According to the dimensions of crossheads in different classes of locomotives made by various builders and master-mechanics, and under the assumption that the maximum steam pressure in the cylinders is 120 pounds per square inch, the writer finds that 50 pounds per square inch of sliding surface is a good average; in a few cases the pressure per square inch was somewhat less than 50 pounds, and in a number of crossheads 75 pounds per square inch was reached. In the writer's opinion 50 pounds pressure per square inch will give very good results, and may be adopted for determining the dimensions of the sliding surface or the gibs of a erosshead which is to be designed. In the following we shall adopt 50 pounds per square inch as the standard. The total pressure of the erosshead against the guides is obtained by Rule 20 or 21. Our next step will be to determine the area of the sliding surface or gibs. RULE 23. Divide the total pressure of the erosshead against the guides by 50 ; the quotient will be the area in square inches of the gibs or sliding surface. EXAMPLE 47. The cylinders in a locomotive are 17 inches in diameter; stroke, 24 inches; steam pressure, 120 pounds per square inch; length of connecting-rod, 7 feet: it is required to find the area in square inches of the erosshead gibs. The area of a piston 17 indies in diameter is 22<>.!>S square indies; the total pressure on the piston will be equal to 226.98 x 120 = 272)17. l pounds. According to Rule 21, the total pressure of the erosshead against the slides will be equal to 27237.6 x i = 3891 pounds. And lastly, according to Rule 23, we have --J};! 1 - = 77.8 square indies for the area of the gibs, or sliding surface of Die crosshcad. The dimensions of erosshead given in Fig. 240 are those of a erosshead in actual use for a 17 x 24 engine, MODERN LOCOMOTIVE CONSTRUCTION. and has given good satisfaction. In this crosshead we find the area of the sliding surface to be equal to (3" + 3") x 14" = 84 square inches. According to our rule, it should have 77.8 square inches. Here, then, is a difference of 6.2 square inches, which is due to the fact that we have made no allowance for the play of the driving box in the pedestal ; this play should have been added to the length of crank ; but when we remember that this size of sliding surface is sometimes used in locomotives having cylinders 18 inches in diameter, we may conclude that the area found according to our rule will give satisfactory results. Assuming that in all locomotives the maximum steam pressure in the cylinder is 120 pounds per square inch, and the ratio of the length of crank to length of the connecting-rod is as 1 to 7, and that the pressure per square inch of the crosshead sliding surface should be about 50 pounds, we may find the area of the sliding surface by the following simple rule : RULE 24. Multiply the area of the piston by the decimal .34 ; the product will be the area in square inches of the sliding surface or of gibs. This rule will give results approximately correct, for all ordinary locomotive prac- tice in which the maximum pressure does not exceed 120 pounds. EXAMPLE 48. What must be the area of the sliding surface of a crosshead for a locomotive having cylinders 20 inches in diameter ? The area of a 20-inch piston is 314.16 square inches; hence 314.16 x .34 = 106.81+ square inches, which is the area of the sliding surface of the crosshead. Com- paring this area with that of the crosshead shown in Fig. 244, we find the area obtained by calculation to be slightly in excess of that in the illustration. TO FIND THE LENGTH AND BREADTH OF THE GIB. 182. Examining the illustrations of the crossheads, we find that the length of each gib is very nearly equal to five times its breadth; in some it is more, in others a little less ; let us adopt the ratio of 1 to 5 as the correct proportion of the breadth to the length of these surfaces. Now, when we know the area of the gib and the ratio of its length to breadth, the dimensions of the latter are easily obtained by the following rule : RULE 25. Divide the area of the surface by 5, and extract the square root of the product ; the answer will be the breadth in inches ; this breadth multiplied by 5 will give the length. EXAMPLE 49. The area of a gib or sliding surface is 45 square inches: it is required to find the length and breadth of the gib. 45 -T- 5 = 9, and the square root of 9 or V9 = 3 inches. Three inches is the breadth, and 3 x 5 = 15 inches is the length of the gib. EXAMPLE 50. What should be the length and breadth of a gib for a crosshead with two guides in a locomotive having cylinders 18 inches in diameter ? The area of a piston 18 inches in diameter is 254.47 square inches. The area of the gib or sliding surface, according to Rule 24, must be 254.47 x .34 = 86.5198 square inches. Then by Rule 25 we have 86.5198 4- 5 = 17.3039 MODEHX LOCOMOTIVE CONSTRUCTION. 165 and ^17.3039 = 4.15 inches for the breadth of the gib ; and 4.15 x 5 = 20.75 inches for the length. EXAMPLE 51. What should be the length and breadth of a gib for a crosshead with four guides in a locomotive having cylinders 18 inches in diameter ! In the solution of this problem it should be remembered that when a crosshead has four guides, as shown in Figs. 234 and 237, the area of the sliding surface is the sum of the areas of two gibs, as F and G in Fig. 257; hence, notice the following solution : The total area of the sliding surface will be 254.47 square inches x .34 = 86.5198 square inches, as in Example 50 ; but, as already stated, this sliding surface is made up of two gibs, hence the area of each gib must be 86.5198 -j- 2 = 43.2599 square inches, then 43.2599 -=- 5 = 8.6519, and V8.6519 = 2.94 inches for the width of gib, say 3 inches ; and 3 x 5 = 15 inches for the length of the gib. Gibs are generally made from inch to inch thick. WIDTH OF CKOSSHEADS AND DIAMETER OF HUBS. 183. In locomotive cast-iron crossheads into which the piston rods are fitted with tapered enils, and sometimes not resting against a shoulder, as shown in Fig. 255A, the area of the hub around the key, as shown in Fig. 256, should be sufficiently large, so fiff. 2SS.I Fig. HS0 froth. -~ a- Fig. 257 that the tensile stress or pull will not exceed 3,000 pounds per square inch of section. This section is, of course, assumed to be taken through D E, Fig. 255A, where the area of the hub will be smallest. Hence, to find the diameter B of the hub, Fig. '256, or the width A, Fig. 12.">7, wo may use the following approximate rule: RULE 26. For cast-iron crossheads, multiply the large diameter of the tapered end of piston-rod, as given in Table 14, by 2 ; the product will be the outside diameter of the hub. "When the piston-rod has no shoulder fitting ;ig;iinst the end of the hub, as shown in Fig. 255A, then make the outside diameter of the hub equal to twice the diameter of the tapered end measured at C that is, the diameter of the hole in the face of the hub. For wrought-iron crossheads multiply the large diameter of the tapered end, or the diameter at C, by 1.8 ; the product will be the outside diameter B of the hub, Fig. 256, or the width A, Fig. 257. 1GG MODERN LOCOMOTIVE CONSTRUCTION. EXAMPLE 52. Find the diameter or the width of a locomotive cast-iron crosshead suitable for four guides, cylinders 17 inches in diameter. According to Table 14, the large diameter of the tapered end of a piston-rod for a cylinder 17 inches in diameter is 2f inches ; hence 2f x 2 = 5 J inches for the outside diameter of hub. EXAMPLE 53. What must be the diameter of the hub of a wrought-iron crosshead suitable for two guides, cylinders 20 inches in diameter? According to Table 14, the large diameter of the tapered end of the piston-rod is 3 inches; hence 3 x 1.8 = 5.4 inches, which is the diameter of hub. The width of the latter class of crossheads will frequently have to be determined by the width of guides, or the length of the crosshead pin. DIMENSIONS OP GUIDES. 184. The guides should be made as short as possible. In practice half an inch for clearance at each end of the crosshead is generally considered to be the least amount that should be allowed. Consequently, if in Fig. 234 the stroke is 24 inches, the length of the sliding surfaces (which in this case is equal to the length of the gibs) is equal to 15$ inches, and the clearance at each end is equal to half an inch, then the shortest distance between the guide-blocks is equal to 24" + 15f " + J" + " = 40^ inches. If to this distance is added the necessary amount for bolting the guide to the guide-blocks, then the shortest length of guides will have been obtained. Sometimes the general design of a locomotive, generally the position of the driving wheels, will compel us to make the length of the guides greater than that determined by the foregoing figures. The breadth of the guide is equal to the breadth of gib or sliding surfaces of the crosshead, according to rules already given. In order to determine the thickness of a guide we must consider it to be a beam firmly fastened at the ends and loaded in the middle. The rule for finding the thick- ness of a beam when all its other dimensions and load are known is as follows: Multiply the length of beam in feet by the load, and divide this product by the breadth in inches multiplied by a constant number. The square root of the quotient will be the thickness in inches. The constant number alluded to is determined by experiment, and is not the same for different kinds of material. From these remarks we would infer, and correctly too, that a different constant should be used for steel than is used for iron beams. But in locomotive practice, for the sake of interchange- ability, it is customary to use the same constant for wrought-iron and steel guides, and this practice we shall follow in these articles. The constant number used in calculat- ing the strength of guides is 1,200. In these calculations we shall, for the sake of simplicity, call the distance between the guide-blocks the " length of the guides." Hence, for finding the thickness of a wrought-iron or steel guide we have the following rule : EULE 27. Multiply the length of the guide in feet by the load in pounds ; divide this product by the breadth in inches into the constant number 1,200 ; extract the square root of the quotient, then the answer, increased by an amount deemed neces- sary for re-planing and wear, will be the thickness of the guide in inches. JfODffR.V LOCOMOTIVE CONSTRUCTION. 167 EXAMPLE 54. Find the thickness of the guides (two guides being used for one crosshead) for a locomotive having cylinders 20 inches in diameter, 24 inches stroke, length of guides 4 feet, breadth of guides 43 inches, length of connecting-rod 7 feet, steam pressure in cylinders 120 pounds per square inch. In the first place we must find the load which these guides will have to support. The load is equal to the greatest pressure of the crosshead against the guide, and consequently can be found by Rule 21. Now, we have for the total steam pressure on the piston, 314.16 square inches x 120 pounds = 37G99.2 pounds, and according to Kule 21, we have 37699.2 x | = 5385.6 pounds of pressure of crosshead against the guides, which is now considered to be the load that one guide will have to support. Now, to find the thickness we have, according to Eule 27, = 3.77; and the square root of 3.77, or V3J7 = 1.9, say 2 inches; 4. t D X j.wUO adding to this J of an inch for truing up, when that becomes necessary through wear, we have 2J inches for the thickness of guide. EXAMPLE 55. Find the thickness of the guides (four guides being used for one crosshead) for a locomotive having cylinders 17 inches in diameter, 24 inches stroke, length of guides 3 feet 4 inches (= 3.375 feet), breadth of guide 3 inches, length of connecting-rod 7 feet, and steam pressure in cylinder 120 pounds per square inch. Area of piston = 226.98 ; hence 226.98 square inches x 120 = 27237.6 pounds total steam pressure on the piston, and 27237.6 x | = 3891.08 pounds, which is the load two guides bearing against the gibs F and G, Fig. 257, will have to support ; conse- quently one guide will have to support 3891.08 n- = 1945.54 pounds, and 1945.54 x 3.375 _ 3 x 1200 L8w ' the square root of 1.82, or ^1.82 = 1.34, say If inches ; add to this i of an inch for truing up, we have 1 inches for the thickness of guides. 185. Sometimes the thickness of the guides is greater at the center of their length than at the ends, as shown in Fig. 241 ; this is done to reduce the weight of the guides ; or, in other words, this form of guide will give the maximum strength with the mini- mum amount of metal. Tapering the guides adds considerably to the expense of labor ; and since the extra weight of guides with parallel faces, or of straight guides, is not objectionable, the writer believes that the latter, such as are shown in Fig. 260, and whose thickness or depth throughout is equal to the thickness at the center of tapered guides having the same work to do, are more desirable to use, and will give as good, if not better, results ; again, observing that the majority of locomotives have straight guides, we are led to believe that many master-mechanics and locomotive builders share our opinion. 186. In determining the depth of a guide for a crosshead requiring one guide only, as shown in Fig. '24X, good judgment must )>< used, Ix-raiise in this case we must not only make the guide sufficiently strong to resist the thrust of the connecting-rod, but 1G8 MODERN LOCOMOTIVE CONSTRUCTION. we must also make it deep enough to guide the end of the piston-rod in a straight line laterally. It should also be remembered that, since guides of this kind will wear on the upper and lower surfaces, we must allow double the amount for re-planing that has been allowed in the other classes of guides ; that is to say, when only one guide is used for a crosshead, then we should allow for re-planing of an inch on the upper sliding surface, and of an inch for the lower sliding surface. Taking these things into consideration, we may employ for determining the depth or thickness of a guide such as shown in Fig. 248 the following rule : RULE 28. Find the depth of the guide by Eule 27 ; add the necessary amount for re-planing, and increase this sum by 25 to 35 per cent, to obtain sufficient depth of guide to keep the piston-rod in a straight line latei-ally. When the crank is turning in the direction of arrow 1, Fig. 260 that is, when the engine is running ahead the weight of the crosshead has a tendency to reduce the thrust of the connecting-rod against the upper guide ; but when the engine is running in the direction of arrow 2 that is, running backward the thrust of the connecting- rod against the lower guide will be increased by the weight of the crosshead. But in locomotives the thickness of the upper guide is always equal to that of the lower one. For extreme accuracy in determining the thickness of either guide, the weight of the crosshead should be taken into account; and furthermore a part of the weight of the guide should also enter into our calculation. For the sake of simplicity, we omitted referring to these items in Eule 27, but they were taken into consideration when the constant number 1,200 was determined upon. Hence these rules should only be used for determining the thickness or depth of locomotive guides, or those for engines of similar design. CASTIB-ON GUIDES. 187. Sometimes locomotive guides are made of cast-iron. In Figs. 258 and 259 we have shown the form and given the dimensions of cast-iron guides working satis- factorily in ten-wheeled engines having 19 x 24 inch cylinders. GUIDE BOLTS. 188. The guides are held in position at one end by the guide-yoke y, Fig. 260, and at the other end they are fastened to the cylinder head. The guide-yoke is made strong enough to prevent the end of the guide moving in a vertical direction, but has not sufficient strength to resist a force acting against it in a horizontal direction, consequently it cannot resist the horizontal force due to the friction between the guides and crosshead. Therefore, for holding the guides in position only one bolt is used at the yoke end, and two bolts are used at the cylinder end. The bolt at the yoke end and one of the bolts at the cylinder end, we may say, are for the purpose of resisting the thrust of the connecting-rod, and the second bolt at the cylinder end is for the purpose of resisting the force acting in a horizontal direction or the pull due to friction between the guides and crosshead. These bolts are generally of an inch in diameter for small locomotives; I and sometimes 1 inch in diameter for larger locomotives ; and occasionally we meet with bolts l-^- inches in diameter for locoino- MODER\ LOCOMOTIVE CONSTRUCTION. 169 tives having cylinders 20 inches in diameter. It is always best to use tapered bolts for this purpose, because these must have a good fit, and if they are made straight, it would require too much labor or the bolt may be ruined in driving it out, when that becomes necessary to take out the thin strips of copper placed between the guide-blocks and guides to take up the wear. It should also be noticed that in locomotives having cylinders of the same diameters but different design of crosshead, the diameters of the guide bolts in the designs such us shown in Figs. 234 and 237 are about the same as those used in the design shown in Fig. 2GO; yet, when we compare the manner of fastening the guides at the yoke end in these designs, it would seem that in the '-.* Fig. 259 design Fig. 260 guide bolts of smaller diameter can be used than in the designs shown in Figs. 234, 237; because in Hie latter two designs some of the thrust of the connecting-rod acts directly against the bolts ; Avhereas in the former design the same amount of thrust seems 1<> act directly against the guide-blocks B B. But a, closer examination of the design in Fig. 260 will make it apparent that, should the guides spring, which may occur, and often does occur, then the thrust will act with a long leverage against the bolt which has but a very short leverage the edge / of the guide- block being the fulcrum and thus greatly increase the stress in the bolt at the yoke end. For these reasons, then, we may assume that the amount of stress in the guide bolts in design Fig. 260 is the same as the amount of stress in the guide bolts in designs Figs. ii:i4 and 237 when the thrust of the connecting-rod in one case is equal to that in the other case. 170 MODERN LOCOMOTIVE COXSTRVCTIOX. DISTANCE BETWEEN THE GUIDES. 189. The distance from a to & between the guides in Fig. 260 (this distance also determines the depth of the crosshead) must be sufficient to clear the connect- ing-rod in any oblique position which it may occupy during the revolution of the crank. Our first step, then, will be to find the position of the guide-yoke y when the length of the connecting-rod, stroke, and length of crosshead are given ; and secondly, we must find that oblique posi- tion of the connecting-rod which will re- quire the greatest distance between the guides. Let L M (Fig. 260) represent the center line of motion of the crosshead pin, and the point x on this line the center of the axle. From the point as a center, and with a radius equal to half the stroke, describe a circle 5 s. 2 s 3 ; the circumference of this circle will represent the path of the center of the crank-pin when the center of the axle is at x. From the point s, at which the circumference cuts the line L M, lay off on the center line of- motion L M a point d ; the distance between the points s and d must be equal to the length of the connecting-rod. From the point d to- wards s lay off a point ; the distance between the points d and H, measured on the line L M, must be equal to the sum of the clearance at the rear end, and the horizontal distance between the center of crosshead pin and the rear end of the sliding surfaces of the crosshead, or the rear end of the gib when one is used; \ also, on the line X M lay off from the point towards s a point v ; the distance be- tween the points n and v must be equal to A< the thickness of the guide-yoke. Through the points u and v draw straight lines perpendicular to the center line of motion ; these lines will represent the inner and outer faces of the guide-yoke, and thus MODERX LOCOMOTIVE OOlTSTBVCTIOJr. establish its position. This position of the guide-yoke is the closest to the cylinder head which it can occupy; sometimes the guide-yoke may have to be moved towards the center of axle in order to clear the driving wheel or to suit other parts of the design. Secondly, to find the oblique position of the connecting-rod which will require the greatest distance between the guides. Through the point x draw a straight line P perpendicular to L M; on this line P lay off above the center x a point # 2 ; the distance between the points x and jr., must be equal to the distance through which the driving box can move before it strikes the frame ; hence the point x 2 will be the cuter of the axle when the driving box occupies its highest position in the pedestal of the frame. Again, on the line P lay off below the center x a point x 3 ; the distance between the points x and x 3 must be equal to the distance through which the driving Itox <-an move before it strikes the pedestal cap; hence the point x 3 will be the center of the axle when the driving box occupies its lowest position in the pedestal. From the point x. 2 as a center, and with the radius equal to half the stroke, describe an arc ef; also, from the point x 3 as a center, and with the same radius, describe an arc .9 It. When the driving box is in its extreme highest position the arc e /will be a part of the path of the center of crank-pin ; and when the driving box is in its extreme lowest position the arc // // will be a part of the path of the center of crank-pin. From the point c 2 at which the line P cuts the arc ef lay off on this arc a number of points c 3 , c 4 , c 5 , C G , c- ; the distance between these points should be about 2 inches or a little less. From these points as centers, and with a radius equal to the length of the con- necting-rod, describe a number of short arcs cutting the center line of motion L M at the points d 3 , rf,, d 7l , rf, ; , <!-. Join by straight lines the points c 3 and (1 3 , c^ and d v c 5 and d 5 , etc. ; then the line c 3 d 3 will represent the center line of the connecting-rod when the crank-pin is at c 3 , and the lines c t d, c 5 d 5 , etc., will represent the center line of con- necting-rod when the crank-pin is at c 4 , c 3 , etc. Now select that center line of the connecting-rod which cuts the inner face i k of the guide-yoke at a point furthest from the line L M. In our illustration the line c 5 d 5 cuts the line i k at the point /, and there is no other line representing the center line of connecting-rod which will cut the line i k at a point above the point 7 ; hence the line c 5 rf r , will represent the center line of the connecting-rod in such an oblique position as will require the greatest distance between the upper guide and the line L M, and consequently the upper guide must be placed high enough to clear the connecting-rod in this position. Above the center line f 5 (1 5 draw a line m n to represent the upper edge of the connecting-rod ; the space between the line c 5 dj an d the line m n must be equal to that between the center line of connecting-rod and its outer edge at a corresponding distance from either end of the rod to the guide-yoke; if the edges of the rod are parallel to each other, then of course the line in n will also be parallel to c :> d-, ; if the rod is tapered, then the line m n must have the same inclination to c 5 d 5 as the edges of the rod have to its center line. The line m n cuts the line I k at the point r, and theoretically the distance between the points u and r would be the required distance between the center line of motion L M and the lower face of the upper guide. But, since small inaccuracies in workman- ship are very difficult to avoid, we must allow some extra space for these inaccuracies; and besides this the ends of the slot in the yoke, shown in Fig. 261, are usually semicircular, and the face of the guide is placed even with the ends of the slot, or, in 172 MODERN LOCOMOTIVE CONSTRUCTION. other words, tangent to the curved part, and therefore some allowance in the distance between the guides must be made to enable the edges of the rod to clear the curved surface in the slot of the yoke. Therefore, above the point r lay off on the line i k a point r 2 ; the distance between the points r and r 2 must be equal to a clearance considered to be sufficient to allow for the inaccuracy of workmanship and the semicircular form of the end O of the slot. In the case before us let the distance between the points r and r 2 be equal to $ an inch. Through the point r 2 draw a horizontal line r 2 a ; this will be the lower surface of the upper guide, and thus the position of the upper guide is estab- lished. Frequently the distance between the centers x and x 2 is greater than the distance between the centers x and # 3 ; Fig. 261 hence it may appear that the distance between the center line L M and the upper guide should be greater than that between the line L M and the lower guide ; but in such cases, after the position of the upper guide has been determined, we simply place the lower one at a distance from L M equal to that from L M to the upper guide. If, on the other hand, the distance between x and x 3 is greater than from x to x 2 , then we must find, by a construction similar to the foregoing, the distance from L M to the lower guide, and place the upper one at the same distance so found above L M, because it is always desirable to have the guides equidistant from the crosshead pin. The construction in Fig. 260 shows plainly that the distance between the guides depends upon the position of the guide-yoke. Again, drawing the connecting-rod in a position so that its center line will be tangent to the path of the crank-pin, as shown by the line c 3 d 3 (Fig. 260), and then making the distance between guides to clear only this oblique position of connecting-rod, as is often done, may result in bringing the guides too close together, and lead to considerable trouble, annoyance, and waste of labor in having to chip the ends of the guides, and increase the length of slot in guide-yoke. PROPORTIONS OF CROSSHEAD PINS. 190. In establishing rules for determining the dimensions of a locomotive cross- head pin it will be best to base these rules on the dimensions of pins used in locomo- tives in actual and successful service. A great difference in the sizes of these pins exists ; but in the writer's opinion the sizes given in Table 15 are a good average, and will be used in establishing the following rules. The greater number of the smaller pins whose dimensions are here given are made of cast-iron, and the greater number of the large pins are made of wrought-iron. MODERX LOCOMOTIVE COXSTRrCTIOX. 173 TABLE 15. AVERAGE DIMENSIONS OF CROSSHEAD PINS AS AT PRESENT USED IN LOCOMOTIVES. Diameter of Cylinder. Stroke. IlilllMftIT Of Croeshead Pin*. Length or CroMhead Plus. 12" 20" 2" 2" 13" 22" 2*" 3" 14" 22" 2f" 3" 15" 22" 2*" 3" 15" 24" 3" 3" 16" 22" 3" 3" 16" 24" 3i" 34" 17" 22" H" 34" 17" 24" 34" 34" 18" 22" 34" 34" 18" 24" 3i" 3i" 19" 22" 3*" 3J" 19" 24" 8t" 34" 20" 24" " 3|" 21" 24" 3f 3f" N ^- s ! fl ft ^"H j | ? \ V ; 7? "<!* ^ , i c t | . i T JF > -< M- 2 "T ^_ } i i ^~ I Fig. 262 Crosshead pins are subjected to a shearing stress, and therefore it would seem that by making the diameter of a pin sufficiently large to give it the necessary strength to resist shearing, and then assigning to it some given length, would be all that is required. But in examining the dimensions given in the table we find the diameters of these pins to be larger than is necessary for their adequate strength. Another notable feature is that the length of the pins is, in all cases excepting three, equal to the diameter. Here, then, we conclude, and s _ rightly too, that there must be other consid- erations besides that of strength which the designers have kept in view in determining the dimensions of these pins. Let us first turn our attention to the length of these pins. We find that their lengths compared with their diameters are less than the lengths of pins ordinarily used in stationary or marine engines. The reason for making the length of a locomotive crosshead pin comparatively so short is that considerable lateral play is allowed between the hubs of the driving wheels and their boxes ; and consequently, when the locomotive is running over a curve the mechanism between cylinders and wheels will become out of alignment, which will create an extra stress on the crosshead pin. Now, in order to reduce this extra stress as much as possible, the pin should be made as short as good practice will allow, and thus reduce the leverage of the pin. Another ivason for making these pins so short is that in many locomotives the space for the crosshead, and consequently its pin, is limited. From these considerations, and also from the dimensions given in the table, it will be seen that the length of a locomotive crosshead pin should be equal to its diameter. By the expression " length of crosshead pin " is meant the length marked L in Fig. 262 that is, the length of that part of the pin which is covered by the connect- 174 MODEMS LOCOMOTIVE CONSTRUCTION. ing-rod brass ; and by " diameter of pin " is meant the diameter marked D that is, the diameter of the same part of the pin. Our next step will be to establish a rule for finding the diameter of the pin. Here a consideration of the greatest importance presents itself, namely, we must not only make the pin large enough to give it the required strength to do the work, but it must also have a large working surface, so as to avoid heating. Right here it may be remarked that when locomotive crosshead pins are correctly proportioned so that they will not heat, they will also have adequate strength for the work, and for this reason we will leave the consideration of strength out of the question. But it must be distinctly understood that these remarks apply only to locomotive crosshead pins, or pins which are as short in comparison with their diameters. The pressure on the piston is transmitted to the crosshead pin, and experience has shown that when the pressure on the crosshead pin exceeds a certain amount the oil will be forced out of the bearing, and consequently heating or abrasion will follow, and the only means at hand to avoid such results is to make the working surfaces sufficiently large to reduce the pressure per square inch. The area of the working surface is estimated by the projected area as shown at A in Fig. 262. This area is always equal to that of a rectangle whose length and breadth is equal to the length and diameter of the pin. Since the pressure per square inch on the pin is estimated by the pressure per square inch on its projected area, we must proportion this area in a manner which will not allow the pressure to exceed a given limit. Here, then, the question arises, what is this limit? To answer this question let us find the projected area of each pin given in Table 15, which is obtained by multiplying the length by the diameter; the product will be the area required. Let us assume that the greatest pressure per square inch on the piston is 120 pounds ; then the total pressure on the piston, and therefore on the projected area of the pin, will be equal to the product obtained in multiplying the area of the piston by 120. Now, dividing this product by the projected area of the pin we will obtain a quotient which will be the pressure per square inch. By so doing we find that the pressure per square inch of the projected area varies from about 2,200 to 3,200 pounds ; and since these pins in Table 15 have given satisfaction, and since their dimensions are suitable for cast-iron pins, and are also often used for wrought- irou pins, we may adopt either 2,200 or 3,200, or any other figure between these two, as a limit or standard of pressure per square inch of projected area. Let us adopt 2,880 pounds per square inch as a standard. We are now in a position to establish a rule for finding the dimensions of any locomotive crosshead pin. RULE 29. Divide the total pressure on the piston in pounds by 2,880 and extract the square root of the quotient ; the result will be the diameter and the length of the pin in inches. Or, putting this rule in the form of a formula, we have, /Area of piston in sq. inches x pressure per inch of piston = diameter and length of CI . OS8 head pin in inches. 2880 EXAMPLE 56. Find the diameter of a locomotive crosshead pin suitable for a MODESX LOCOMOTIVE COXSTRTCTIOX. 175 cylinder 18 inches in diameter, and a steam pressure of 120 pounds per square inch of piston. Area of 18-inch piston = 254.47 ; hence, LT.4.47 x li'O "2880" :1 - 60; mid the square root of 10.60 is 3J (nearly) ; therefore the diameter of the pin will be 3} inches, and the length will also be 3J inches. In a similar manner we can obtain the dimensions of the crosshead pins for all locomotives when the diameter of cylinder and steam pressure is given. But if we assume that in all locomotives the maximum steam pressure per square inch of piston is 120 pounds, then the foregoing rule can be made simpler, and we obtain the following : RULE 30. Divide the area of the piston in square inches by 24, and extract the square root of the quotient ; the answer will be the diameter and length of the cross- head pin. Or, putting this rule in the shape of a formula, we have, 'Area of piston in square inches 24 = diameter and length of crosshead pin in inches. By this last rule the dimensions of the crosshead pins in Table 16 have been obtained. As will be seen, the dimensions of pins in Table 16 agree very closely with those in Table 15, and may therefore be adopted as the standard sizes of cast-iron pins for locomotives in which the steam pressure in the cylinders does not exceed 120 pounds per square inch. A number of locomotive builders make the diameters of wrought-iron pins somewhat less than that of cast-iron ones, but leave the length of the former the same as that of the latter. But, on the other hand, quite a number of builders make the diameters of cast-iron and wrought-iron pins alike, and thereby obtain a greater uniformity in the patterns for the connecting-rod brasses. TABLE 16. DIMENSIONS OF CROSSHEAD PINS SUITABLE FOR LOCOMOTIVES IN WHICH THE STEAM PRESSURE PER SQUARE INCH DOES NOT EXCEED 120 POUNDS. Diameter of Cylinder*. Diameter of Croeshead Pins. Length of Croeshead Pint. 9" If If 10" " If 11" 2" 2" 12" 8j" 2f 13" 2f 2f 14" 2|" 2f 15" 2f" 2f" 16" 2S" 2f 17" 3" 3" 18" 3f 3i" 19" 34" 3f 20" 3f 3f 21" 3i" 3J" 22" H" 3f 176 MODERN LOCOMOTIVE COXSTUVCTION. REMARKS RELATING TO THE FORM OF CROSSHEAD PINS. 191. Cast-iron pins are cast to the crosshead ; wrought-iron or steel pins are put in separately, and fit into tapered holes in the crosshead. The taper of these holes should not be too great, as an excessive taper will throw too much stress on the nuts and is liable to tear the pin at 7?, Fig. 262. A good taper, and one which is often used, is 1J inches in 12 inches that is, the diameter of one end of the 12 inches will be l Fig. 263 Fig. 264, inches less than at the other end. Many master-mechanics use one taper reamer only, as shown in Fig. 263, for reaming both holes which fit the pin at C and F. Some master-mechanics object to this plan, because in their opinion it does not leave a shoulder sufficiently large at E, and therefore the diameter of the pin at C is reduced, although the taper per inch is left the same as before. For pins of this kind a step reamer similar to that shown in Fig. 264 will have to be used. The crosshead pin is held in position by two nuts N N, and to obtain further security a split pin P is inserted in the end of crosshead pin. All crosshead pins should be prevented from turning by a dowel pin or a small feather, as shown at C. Crosshead pins made of wrought-iron should be case hardened. STUFFING BOXES AND GLANDS. 192. The purpose of the stuffing box and gland is simply to hold some kind of packing close against the piston-rods, valve-rods, or spindles of valves, etc., thus forming a steam-tight passage for the rods or spindles. The packing may be divided into two distinct classes, namely, metallic packing and hemp packing. In the latter we include all packing made of fibrous material. Most of the metallic packing at present in use is manufactured by firms who make the manufacture of it a special business, and these firms furnish the dimensions of the stuffing boxes to hold this packing ; hence the only kind of stuffing boxes to be considered here will be those which are to hold hemp packing. Fig. 265 represents a stuffing box with gland similar to those cast to locomotive cylinder heads. Fig. 266 represents a stuffing box with gland similar to those cast to locomotive steam chests. Fig. 267 represents a stuffing box with screw-cap, as is generally used for small valves, cocks, etc. In order to find the principal dimensions of the stuffing box, glands, and studs, the following rules may be used ; and the dimensions thus obtained will agree with good practice : RULE 31. To find the thickness t of the stuffing box shown in Figs. 265 and' 266, AIODEHX LOCOMOTIVE COSSTBVCTION. 177 Add | of an iuch to i the diameter of the rod ; the sum will be the thickness of the stuffing box at t. EXAMPLE 57. Find the thickness at t for a piston-rod stuffing box, the piston-rod being 24 inches in diameter. | diam. + of an inch = thickness ; hence, I" + i" = ", thickness at t. EXAMPLE 58. What should be the thickness at t for a valve-rod stuffing box, the valve-rod being 14 inches in diameter? hence, J of 14. inches = f ; I" + 1" = f", thickness at t. In practice the thickness at t, Fig. 266, is about 4. inch for small valve-rods, and of ail inch for the large valve-rods. The thickness at t for piston-rod stuffing boxes, Fig. 265, ranges generally from 3 inch for small piston-rods and 1 to If inches for the larger ones. The thickness of the stuffing-box flange / should be sufficient to obtain a good depth of thread for the studs ; hence, to find thickness / of the stuffing-box flange, we have the following rule : RULE 32. To i of the diameter of the rod add 8 of an inch, and increase this sum 25 per cent. This sum will be the thickness of the stuffing-box flange. Putting this rule in the shape of a formula, we have, diameter of rod 4- inch diameter of rod + | inch == thickness of the stuffing-box flange. EXAMPLE 59. Find the thickness of a valve-rod stuffing-box flange, the rod being 14 inches in diameter. J of 14. inches = | inch ; hence, 3" + 8" I" + |" + 1-= - = U inch thickness of flange. 178 MODERN LOCOMOTIVE CONSTRUCTION. The flange of the piston-rod stuffing box, Fig. 265, generally forms part of the cylinder head casing, and therefore it is often made from 14 inches to 16 inches in diameter. The guide-blocks are also fastened to this flange, and consequently its thickness cannot be exactly determined by the foregoing rule ; the thickness of the flange near the body of the box will always be more than that obtained by this rule. In large engines the thickness of this flange will often be from If to 2 inches, and this thickness extends from the stuffing box to beyond the guides; and from the guides to the edges of the flange, its thickness is reduced to about inch. 193. For determining the packing thickness p we may employ the following rule : EULE 33. To J of the diameter of the rod add J of an inch ; the sum will be the thickness p of the packing. Putting this rule in the shape of a formula, we have, i diameter of rod + J inch = thickness p of packing. EXAMPLE 60. Find the thickness of the packing in a stuffing box for a valve-rod, the rod being 1 inch in diameter. J" + 4" i inch for the thickness of the packing. EXAMPLE 61. Find the thickness of the packing in a piston-rod stuffing box, the piston-rod being 3^ inches in diameter. 3i" + i" = IfV inches for the thickness of packing. In good locomotive practice we find the average thickness of packing for rods of small diameter inch, and for large piston-rods 1& inches. Here we see that the dimensions obtained by the rule agree with practice. If the rods are larger than 3J inches in diameter, this rule cannot be used, because the thickness of the packing so found will be too great. But, since locomotive piston-rods are seldom larger than 3 inches in diameter, we may conclude that the foregoing rule can be used for finding the thickness of the packing in all stuffing boxes iised in locomotives. As soon as we know the thickness of the packing, the diameter 7 of the stuffing box is readily obtained, for we have only to add twice the thickness of the packing to the diameter of the rod ; the sum will be the diameter /. 194. Generally speaking, the greater the depth H of the box the longer the engine will run without renewing the packing. In locomotives the depth // of the piston-rod stuffing boxes is often limited, therefore the general practice is to make this depth equal to 1^ to 1J times the diameter I of the stuffing box ; this proportion of diameter to the depth of the box is also adopted for the valve-rod stuffing boxes. 195. Stuffing-box glands for the valve-rod are sometimes made of brass, and many are made of cast-iron ; piston-rod glands are nearly always made of cast-iron. In order to reduce the number of patterns as much as possible, and also to reduce the number of tools and templets necessary for boring and turning the glands, the dimensions of a brass gland and a cast-iron gland are alike ; hence the following rules apply to glands made of either metal : For valve-rods of small diameter the glands are often made entirely of brass, as shown in Fig. 266. When the larger glands are made of cast-iron, they are lined with a brass bushing (Fig. 265) in the same way as all large glands are lined where the cost MODERN LOCOXOTirE COXSTRrCTIOX. 179 of labor in making the bushing is less than the cost of making the gland entirely of brass. In the smaller oast-iron glands the bushing is generally inch thick, and in larger glands ^ inch thick. The end b. 2 of the bushing is enlarged; some- times this enlarged part will cover the whole end of the gland as shown, and this the writer believes to be the best practice; at other times the diameter of this end is only a very little larger than the diameter of the bushing, the cast-iron part being counterbored to receive the enlarged end. The bushing is forced into the cast-iron ; its object is to prevent the collection of rust on the inside of the gland when the engine stands still for any considerable length of time, and thus prevent scratching or injuring the rod. 196. For finding the thickness g of the flange on gland, Fig. 265, we may use the following rule : RULE 34. To J of the diameter of the rod add f of an inch ; the sum will be the thickness g of the flange. EXAMPLE 62. Find the thickness of the flange on a piston-rod gland, the rod being 3 inches in diameter. |" + |" = i inches for the thickness of the flange. The flanges on the piston-rod gland are generally made oblong in form, as shown in Fig. 268 ; sometimes oil chambers are cast in these flanges, as shown in Fig. 269 ; the thickness of the latter flanges is somewhat greater than the thickness obtained by Fly. 27O Fig. 268 Fly. 269 the rule. The flanges on the valve-rod glands are generally circular in form, as shown in Fig. 270. The length (Fig. 268) of the piston-rod gland, and the diameter of the valve-rod gland (Fig. 270) must be made sufficiently great to allow the edges of the flanges to project a little beyond the nuts of the studs. The length of the gland measured from the flange to the end is generally made equal to if or of the depth H of the stuffing box. 197. A brass ring d, as shown in Fig. l2<>.">, is placed inside of the stuffing box. The hole in this ring is just large enough to allow the piston-rod to pass through easily, whereas the hole e through the cylinder head, or, in other words, the hole e through that portion of the cast-iron which forms one end of the stuffing box, is generally made J inch larger in diameter than that of the piston-rod. This ar- rangement prevents iron and iron from touching each other, and consequently what 180 MODERN LOCOMOTIVE CONSTRUCTION. little rust may form and collect in tlie hole e through the cylinder head cannot scratch or injure the rod. Sometimes we find the brass ring d extending through the cylinder head ; in cases of this kind the form of the ring d will be similar to that of the ring d shown in Fig. 266. Allowing the ring d to pass through the cylinder head in this manner is, in the writer's opinion, bad practice, because this ring is liable to break, and sometimes it does break; then if pieces of it fall into the cylinder, more or less damage to the cylinder head or piston may be the result ; the writer has known accidents of this kind to happen, incurring a great expense for repairing the damage. Although brass rings d similar in form to that shown in Fig. 266 should not be used in any kind of stuffing boxes, the use of this form of ring cannot be avoided in a valve-rod stuffing box for the following reason : The valve-stem is forged to the valve yoke, and therefore it must be entered into the stuffing box from the inside of the steam chest; this cannot be done without canting the valve-stem, because the form of the steam chest will not allow it to enter the hole squarely, and consequently this hole must be considerably larger in diameter than that of the valve-stem; when the stem is in position the hole is reduced by the brass ring d, hence this shape. From the fact that a large hole is required for entering the valve-stem into the stuffing box, it will be readily perceived that the valve-stem cannot be taken out of the steam chest or placed into the same without first removing the ring d, and therefore this ring must not be fitted very tightly in the stuffing box. The face of the i-ing d and the end of the gland which touches the packing are generally turned slightly concave, so as to help to force the packing against the rod. 198. To keep the packing in place, and to compress it sufficiently to prevent leakage, the gland must be forced against the packing, and for this purpose the studs c c (Figs. 265 and 266) are used. In the piston-rod stuffing box two studs are generally employed; the limited space for the gland prevents the use of a greater number of studs. In the valve-rod stuffing box two or three studs are used, the number of studs depending on the fancy and judgment of the designer. In the piston-rod stuffing box the studs should be placed sufficiently far apart to allow the hub of the crosshead to pass between the nuts on these studs. In the valve- rod stuffing box the distance from the center of the studs to the center of the box should be sufficiently great to allow the tap to pass the outside of the box when the holes for these studs are being tapped. For finding the diameter of these studs. when two are used in each box we have the following rule : RULE 35. To J of the diameter of the rod add ^ inch; the sum will be the diameter of the stud. Putting this rule in the shape of a formula, we have, 4 diameter of rod + 4 inch = diameter of stud. EXAMPLE 63. Find the diameter of the studs for a piston-rod stuffing box, the rod being 3 inches in diameter. f " + J" = 1 inch for the diameter of the stud. The same rule may be used in finding the diameter of the studs for the valve-rod stuffing box when three studs are used for each box ; although, theoretically, when MODERN LOCOMOTirE COXSTRUCTIOX. 181 more than two studs are employed, the diameter of each stud can be made somewhat less than that found by the rule. The general practice is to make all studs for small piston-rod stuffing boxes inch in diameter; for piston-rod stuffing boxes on cylinders 12 inches in diameter and up to 17 inches in diameter " studs are used; for cylinders 18 to 20 inches in diameter 1" studs are used; and for larger cylinders Ij" studs. For the valve-rod stuffing boxes the diameter of the studs varies from f to J inch, according to the size of the rod. Two nuts are always used for each stud; often both nuts are placed outside of the gland, as shown in the illustrations, but sometimes the nuts are placed so that one will be outside, and the other nut inside of the flange g. These nuts are case hardened to prevent their corners from becoming worn ; and for the sake of convenience (so that one wrench can be used) the nuts for the piston-rod gland and those for the valve-rod gland are made the same size, even when larger studs are used for the former than for the latter. When only two studs are employed great care must be taken to have the center of the studs and the center of the rod in one straight line, otherwise trouble will be experienced in screwing up the gland ; in fact, when the two studs cannot be placed exactly in line with the center of the rod it is better to use three studs. Another manner of compressing the packing is shown in Fig. 267. Instead of having a gland, we have here a brass sleeve a fitting the rod and the inside of the stuffing box. This sleeve is pressed against the packing by means of the nut 6, which is tapped to fit the thread cut on the outside of the stuffing box d. It will be noticed that the sleeve a has a small flange on top; the purpose of this flange is simply to prevent the sleeve from being pressed too far into the box, and to provide some means of pulling it out of the box. CHAPTER V. FRAMES. AXLE BOXES. FRAME PEDESTALS. 199. The figures numbered 2*71 up to 279 represent the proportions of frame pedestals for passenger locomotives of different sizes. The function of the pedestal is to hold the axle box often called the driving box at a given distance from the cylinder, but in the meantime allowing the axle box to move in a vertical direction. The pedestals are made of wrought-iron, and each one, as shown in Figs. 271 and 280, consists of a portion of the upper frame brace B, the pedestal legs A A 2 , and the mechanism used for preventing an increase of the opening at the bottom of the jaw. The three parts, namely, the portion B of the frame brace and the two pedestal legs A A. z , form what is called the pedestal jaw. The pedestal legs in large locomotives are often connected at the bottom by the bolt D passing through a frame thimble T inserted in the opening of the jaw, as shown in Fig. 271 ; in smaller engines the legs are connected by a pedestal cap C as shown in Figs. 277, 278, 279, and also in 280. The frame thimbles T are made of cast- iron, the caps C are made of wrought-iron. The reason for not using the bolts D and frame thimbles in smaller locomotives is that the bolt D will interfere with the wedge bolt E, as will be presently explained. The pedestals are united in each frame by the upper frame brace B 2 and the lower frame brace L ; these braces are forged to the pedestal jaws. There are two distinct forms of pedestal jaws used ; one is represented in Fig. 271 and the other in Fig. 280. The difference between these two forms consists in the shape of one of the pedestal legs, thus : The jaw represented in Fig. 271 has one straight and one tapered leg that is to say, the inside of one of the pedestal legs, as A 2 (called the straight leg), is planed square with the top of frame, the inside of the other one, A, is planed so as to form an angle with the top of frame, making the opening at the bottom of the jaw greater than at the top. In the pedestal rep- resented in Fig. 280 both legs are tapered. The form of pedestal shown in Fig. 280 has been used very extensively in former years; but lately the use of the form shown in Fig. 271 has increased. Some master-mechanics prefer to use for all locomotives the pedestal caps as shown in Figs. 277, 278, and 279 in place of the cast-iron frame thimbles T and the bolts D; but the writer believes that the use of the thimble and bolt will add to the stiffness of the pedestal, because by the use of the bolt D the lower frame brace L will be brought nearer in line with the LOCOMOTIVE CONSTRUCTION. 183 r-f-tt n i ... * Lf 184 MODERN LOCOMOTIVE CONSTRUCTION. >* center of driving axle; by so doing a better dis- tribution of metal in the frame is secured and the stiffness of the pedestal legs increased. WEDGES. 200. The function of the wedges shown in section, and marked W W 2 in Fig 271 is twofold: first, they protect the pedestal legs from wear ; sec- ondly, with these wedges the play is taken up be- tween the axle box and the wedges caused by the wear, which will result from the vertical movement of the axle box. The wedge marked W is called the " short wedge," and that marked W 2 is called the "long wedge." It may here be necessary to remark that the long wedge W 2 in this pedestal has in nowise a wedge shape, consequently "a shoe" would be a better name for it; we shall for the sake of simplicity follow the usual custom and re- tain the term "wedge," as this term will cover both wedges used in the pedestal shown in Fig. 280, in which the long wedge W 2 must necessarily have the shape of a wedge similar to that of the short one. The wedges must be accurately fitted in the pedestal jaw, so that the wearing surfaces s s and s 2 s 2 of these two wedges will be exactly parallel to each other, and perpendicular to the top of the frame ; the distance between these wearing surfaces should be equal to the width of the axle box. LONG WEDGE. 201. The long wedge is always fitted to the straight pedestal leg, and since the wearing surface s 2 s 2 (Fig. 271) of the wedge must stand perpendic- ular to the top of frame, it follows that the thick- ness of the metal forming the wearing surface s 2 s 2 must be the same throughout. The length of the wedge W 2 is equal to the distance between the top of the thimble T and the bottom of the frame brace B, so that this wedge cannot move in a vertical direction, and it is further secured in position by the screw bolt R 2 , which holds the wedge firmly against the straight leg. In order to prevent on the long wedge the formation of ridges, the thick- ness of the metal at the ends is reduced, causing MODERN LOCOMOTIVE CONSTRUCTION. 185 the wearing surfaces on three sides of the wedge to project beyond the metal at the ends, and these projecting surfaces are accurately planed. The long wedge is shown in .Mail in Figs. 281 and 282. SHOUT WEDGE. 202. A reduction of the metal at the ends of the short wedge W (Fig. 271) is not necessary, because the length of the wedge is always made equal to, or a little less than, the length of the axle box, and consequently ridges cannot be formed on it, as the axle box in its vertical movement will move beyond the ends of. the -Bz - - 13V Fig. 280 O g. ssi U O ' 11 i O J'i'j. SSa J-'lg. 287 fig. XS3 *''(/ * Tig. USB Tiff. HS8 wedge. Since the wearing surface s s must be perpendicular to the top of frame, and since this wedge has to fit the tapered pedestal leg, it follows that the part of it against which the side of the axle box slides must have a wedge form, as shown. The play between the wedges and the axle box is taken up by moving the short wedge upwards by means of the wedges bolt K. By so doing the short wedge will slide against the inner surface of the tapered pedestal leg A, and thereby reduce the distance between the wedges. When the short wedge has been adjusted to the correct position, it is held there by the wedge bolt E, and also by the screw bolt R, which holds it firmly against the pedestal leg. For the bolt R a slot is cut in the leg, so MODERN LOCOMOTIVE CONSTRVCT10X. that the bolt can be moved up or down with the wedge to any desired position. The short wedge is shown in detail in Figs. 283 and 284. WEDGE BOLTS. 203. When a cast-iron thimble is used, as shown in Fig. 271, two wedge bolts Z? are employed for each short wedge. These bolts pass through slots m n, Fig. 273, cast into the thimble near the end, one on each side of the bolt D. The reason for casting slots near both ends of the thimble, as shown, is to make the thimble revers- ible. The heads of the wedge bolts are cylindrical in form, as represented in Fig. 285. These heads fit into recesses //cast in the short wedge, as shown in Fig. 283. In small locomotives the frames are not sufficiently wide to admit two wedge bolts and therefore only one can be used, and this bolt must be placed in the center of the wedge, as indicated by the recess / in the wedge shown in Fig. 286. But placing the wedge bolt in the center of the wedge will prevent the use of a pedestal bolt I), which must also pass through the center of the pedestal legs, and therefore these two bolts will interfere with each other. It is for this reason that in small locomotives wrought-iron pedestal caps (7, as shown in Fig. 277, are employed in place of the cast-iron thimble T and pedestal bolts D. In the writer's opinion it is always best not to tap the pedestal caps for the wedge bolts E, but to allow this bolt to pass through a slot cut in the pedestal cap. In this case the wedge bolt will have the same form of head as shown in Fig. 285. If the pedestal cap is tapped for the wedge bolt, then the head of this bolt must have a conical form, as shown in Fig. 288. PROPOKTIONS OF WEDGES AND BOLTS. 204. We have already stated that the length of the long wedge must be equal to the length of opening in the pedestal ; and the length of the short wedge equal to the length of the axle box, or a little shorter. In the long wedge the thickness of the metal which forms the wearing surface s 2 s^ should not be less than that given in the illustrations ; and the thinnest part of the short wedges should be about inch for small locomotives, and f inch for large ones. The flanges of all the wedges in small locomotives should not be less than f inch thick, and for larger ones l inches thick ; the exact thickness of these flanges for the different sizes of axle boxes, and which the writer would recommend, are given in Figs. 316 to 340. The diameter of the wedge bolts E is usually inch for the small locomotives, and I inch for larger ones. The bolts which hold the wedges to the pedestal legs are generally made inch in diameter. 205. All the principal dimensions of the pedestals for passenger locomotives are given in our illustration, and these dimensions agi'ee with modern locomotive practice. In connection with this subject it may here be remarked that in late years the mechanisms of the larger locomotives have been made heavier and their weights increased. It will therefore be found by comparison that the dimensions of the larger pedestals will exceed the dimensions of pedestals made a few years ago, and the dimensions given for the smaller pedestals will agree very closely with the MOI)K1!\ LOCOMOTIVE CONSTRUCTION. dimensions of the average pedestals now in use. The dotted circle, with the diameter given in each ped- estal, represents the driving axle journal suitable for each one of these pedestals. It will be noticed thtit the diameter of the journal given in Fig. 271 is considerably larger than the average diameter of journals used in passenger locomo- tives built some years ago ; but in modern engines of this class jour- nals as large as shown in this fig- ure are now used, and the writer believes it is only a matter of time when this size of axle will be gen- erally adopted for fast passenger engines having cylinders 18 inches in diameter. ENGINE FRAMES. 206. Fig. 289 represents the main frame for an eight-wheeled passenger engine, such as is shown in Fig. 1, and suitable for a locomo- tive having cylinders 18 inches in diameter. Fig. 290 represents the front splice of the same frame ; the front splice is fastened to the main frame, as shown in Fig. 289, in which that portion marked S rep- resents one end of the front splice. Fig. 291 represents the main frame for a locomotive of the same class as the foregoing, but having cylinders 10 inches in diameter. The back ends of these main frames, Figs. 289 and 291, aiv suit- able for a footboard, and, since nearly all locomotives which carry footboards burn soft coal or wood, it may be said that these frames are for soft coal and wood burning locomotives. For this class of lo- comotives the horizontal distance OS 8 * i I 188 MODERN LOCOMOTIVE CONSTRUCTION. from the center of the rear axle to the back end of frame is usually 42 inches. For hard coal burning locomotives this distance may have to be changed, and made either longer or shorter to suit the design of boiler. In designing a locomotive frame the first step is to locate the centers of the driving wheels and the position of the cylinders. It may be said that the relative position of the driving wheels and the cylinder depend upon the proper distribution of the weight on the drivers, and also on the length of the boiler. Again, in all eight- wheeled passenger engines, such as shown in Fig. 1, ten-wheeled engines, shown in Fig. 2, and mogul engines, shown in Fig. 3, which are designed for burning soft coal or wood, the fire-box is placed between the two rear axles, and consequently the distance between these axles must be sufficiently great to admit the fire-box between them ; there must also be sufficient room for the working of the eccentrics, space for the axle boxes, room enough for cleaning the water space around the furnace, and such space as may be required for other special mechanism which the design of the locomotive may call for. But in the meantime it must be remembered that the distance between the centers of any two wheels which are connected by a side rod must not exceed 8' 9" or 9' 0" at the utmost ; the latter distance is seldom used. If the distance between the centers of the driving wheels exceed these distances, the length of the side rods will become too great, and consequently dangerous ; because, on account of the great number of revolutions per minute of the driving wheels, the change of motion of the side rods from an upward to a downward or from a downward to an upward motion becomes so sudden that the weight of the rods will be an element of danger, causing the side rods which are longer than 8' 9" or 9' 0" to Tae shaken to pieces. From these remarks we learn that in the classes of locomotives before mentioned the greatest distance between the center of the rear driving wheel and the center of the one next to it is limited by the length of the side rod, and the shortest distance between the centers of the same drivers in the same classes of engines is limited by the length of the fire- box. In ten-wheeled locomotives the distance between the center of the middle driving wheel and the center of the front one depends greatly upon the general design of the engines ; but usually the position of the front drivers in these engines is determined by that of the front truck, and sometimes by the valve motion. In all ten-wheeled engines that have come under the writer's notice, the distance between the centers of the middle and front drivers has been less than that between the centers of the rear and middle drivers. In mogul engines, the front driving wheels are generally placed as far forward as the cylinder will permit, leaving just room enough for removing the cylinder head and casing without striking the tire. In these engines, too, the distance between the centers of the middle and front drivers is generally less than that between the centers of the middle and rear drivers. In consolidation we have the first, second, third, and fourth pair of driving wheels ; the pair of driving wheels next to the cylinder is called the first pair. The same conditions which determine the position of the front drivers in a mogul engine will also determine the position of the first pair of drivers in the consolidation engine ; that is, in these engines the front drivers are placed as far forward as the cylinders MODERX LOCOMOTIVE CONSTRUCTION. will permit, so that the cylinder head and casing can readily be taken off. The distance between the centers of the first and second pair of drivers must be sufficiently great to admit the rocker between the tires of these wheels. The distances between the centers of the second and third pair, and between the third and the fourth pair, are generally arranged so as to leave 1 inch or 1J inches clearance between the nanges of the tires. 207. In small locomotives the total wheel base generally depends on the proper distribution of the weight of the engine on all the wheels. For instance, moving the front truck nearer to or further from the center of gravity of the locomotive, we throw more or less weight on the truck. In larger engines we may often, if it is desirable, be able to move the front truck nearer to the center of gravity of the loco- motive ; but if we attempt to move the truck away from the center of gravity of the engine, we may meet with obstacles, namely, the sharp curves of the track over which the engine has to run, and for which the wheel base must be kept as short as possible. The turn-tables of the road may also limit the length of the wheel base. Therefore it will be seen that the arrangement of the wheels, and the determination of the total wheel base of large locomotives, is brought within very narrow limits. And it may be said that, in cases of this kind, the ingenuity of the designer is often taxed to the utmost to obtain satisfactory results ; and even then he may have to be satisfied with results not as desirable as they should be. 208. The relative positions of the wheels under hard-coal burners are some- times the same as those under soft-coal burners ; at other times conditions will arise which will compel a change in the arrangement of the wheels under the hard-coal burners. DEPTH OF PEDESTAL. 209. The depth of the pedestal that is, the distance D, Fig. 289, from the top of the cast-iron thimble to the under side of the upper frame brace B should be suf- ficient to allow the driving box to move a given amount in a vertical direction, thus: In Fig. 289 the line marked F represents the top, and the line marked G, the bottom of driving box. The depth of the space between the top of the box and the frame brace B, plus the depth of the space between the bottom of the box and the thimble, represents the total vertical movement of the driving box. When a locomotive is in good working order, with the usual amount of fuel and water, the driving box should occupy in the pedestal a position in which the upper clearance that is, the space between the top of box and frame brace is greater than the lower clearance, or the space between the bottom of the box and thimble. Thus: In Fig. 289 we see that the upper clearance is 3 inches, and lower clearance is 1A inches. The total amount of clearance and the difference between the top and bottom clear- ance is arbitrary and is not always alike in the same class of locomotives. The average amount of clearance at the top and bottom of the boxes for the different sizes of locomotives, as generally adopted by locomotive builders and master- mechanics, is given in Figs. 271 to 279, in which the dotted lines immediately over and under the axle represent the top and bottom of the driving boxes; the dimen- sion given from the top of the box to frame brace B represents the amount of 190 MODERN LOCOMOTIVE CONSTRUCTION. the upper clearance, and the dimension given from the bottom of the box to the thimble or pedestal cap represents the amount of the lower clearance. WIDTH OF PEDESTAL OPENING. 210. The width of the opening of the pedestal, or the distance from leg to leg, Fig. 289, should be such as will not admit the short wedge further into the ped- estal after the driving box and long wedge are in position than is necessary for it to clear the wedge-bolt nut on the top of the thimble, leaving as great a distance as possible between the top of the short wedge and the frame brace B, through which the short wedge can be moved to take up the play. The distance H given in Fig. 289, from the center line x Y to the face of the short wedge, represents one-half the width of the driving box ; and so also the dimensions from the vertical center lines to the face of the short wedges in Figs. 271 to 279 represent one-half the width of the axle boxes. TAPEK OF PEDESTAL LEGS, AND POSITION OF STKAIGHT LEG. 211. When pedestals are used like those shown in Figs. 289 and 291, the straight leg should always be placed towards the cylinder; by so doing the distance from the cylinders to the center of the driving wheels cannot be readily changed, and therefore the distance from center to center of the brasses in the main rod need not be so often adjusted. The amount of taper for the inner surface of the tapered legs is generally l inches in 12 inches ; and this taper is used for all pedestals of the form shown in Figs. 289, 291, and 280. POSITION OF CENTEK LINES. 212. In connection with this subject it may be advantageous to the reader to call his attention to the fact that when pedestals such as shown in Figs. 289 and 291 are used, the vertical center line drawn through the center of the axle does not pass through the center of the opening of pedestal at the top ; that is to say, the distance K (Fig. 289) from the center line x Y to the straight leg will be greater than the distance / from the center line a; I 7 " to the top of the tapered leg ; at the bottom of the pedestal the conditions are reversed. When pedestals such as shown in Fig. 280 are used, the vertical center line drawn through the center of the axle will pass through the center of the opening of pedestal, both at the top and bottom. It is well to note these facts, because in designing a frame the position of these center lines have a very important bearing in determining the position and dimensions of other parts of the locomotive. Hence in designing a frame having pedestals as shown in Figs. 289 and 291, the distance from the straight pedestal leg to the vertical center line x Y must be equal to the thickness of the long wedge added to one-half the width of the driving box, whereas for the pedestals shown in Fig. 280, the vertical center line must be drawn through the center of the opening of the pedestal. In all pedestals the horizontal center line drawn through the center of the axle must be in a position which will give about the same relative clearance on top MODERN LOCOMOTIVE CONSTRUCTION. 191 and bottom of driving box as given in Figs. 271 to 279 ; or, in other words, in design- ing a locomotive frame the driving boxes must be drawn in the same positions as they would occupy when the engine is in first-class working order and running on the road; and the boxes must be considered to be stationary during the time the locomotive is being designed. WIDTH OF FRAME. 213. For small locomotives the width of frame should not be less than 3 inches, so as to provide on top of frame a surface sufficiently wide to which the rocker box, lifting-shaft bearings, and other mechanism can be bolted without interfering with the necessary strength of the frame. In large locomotives the space between the driving wheels and the fire-box will limit the width of the frame, and is seldom, if ever, wider than 4 inches. We may therefore conclude that the width of locomotive frames ranges from 3 to 4 inches ; the suitable width of frame, such as is usually adopted for any one of the different sizes of passenger locomotives, will be found in Figs. 271 to 279. .x 1 DIMENSIONS OF FRAME BRACES. 214. To the upper frame brace B., in Fig. 292 (also see Figs. 271 and 274) are bolted and attached some of the principal parts of the locomotive. The forces acting upon the braces are of a complex character, and therefore to find the exact dimensions of the braces, which will give them the required strength no more and no less to resist the forces acting upon them, would be a very difficult matter. Consequently, rules which are to be of any practical value for finding the dimen- sions of a locomotive frame, can only be empirical or arbitrary rules. The following rules are founded upon the observation of the writer, and he believes that the results obtained by them will agree with the best practice. We have already established the width of the frames for the various sizes and classes of locomotives ; our next step will be to find the cross-sectional area of the upper f runic brace !'>.,. One of the principal forces to which locomotive frames are subjected is the pulling force, or the horizontal force, which acts parallel to the frame braces B. 2 and L. This pulling force is not equal to the total steam pressure on the piston, but for the sake of simplicity in establishing the following rules, and for convenience in finding the dimensions of other locomotive frames, we may assume it to be so, without falling into any serious errors. Therefore we will again assume, as before, that the maximum steam pressure in the cylinder is 120 pounds per square inch. Comparing the total steam pressure on the piston with the cross-sectional area of the frame brace I3 2 in the frames lately made, we find that when the cylinders are 11 inches and up to 18 indies in diameter, then 1 square inch for every 2,000 pounds of the total steam pressure on the piston is allowed in the cross-sectional area of the frame braco /?.,; for cylinders 19 and 20 inches in diameter, 1 square inch for every 2,200 pounds; for cylinders _'] and 22 inches in diameter, 1 square inch for every 2,400 pounds; and for cylinders Hi 192 MODERN LOCOMOTIVE CONSTRUCTION. -IB- S' inches and less in diameter, 1 square inch for every 1,700 pounds of the total steam pressure on the piston is allowed. According to these figures, it will be seen that the cross-sec- tional area of the smaller braces is greater than that of the larger braces, when these are compared with their respective piston press- ures. This is as it should be, because the ratio between the depth and width of the smaller braces, or, we may say, the distribution of the metal in the smaller braces, is not as good for obtaining the necessary strength to resist the forces which act in a vertical direction as the distribution of the metal in or the ratio between the depth and breadth for the larger braces, and therefore the larger frame braces can resist all the forces acting upon them with comparatively less metal than the smaller ones. It may be asked : Why cannot we make the form of cross-section in smaller frames similar to that of the larger ones? To this we answer that the widths of the frames are determined by certain conditions, as explained in Art. 213, and cannot be changed ; therefore if we attempt to make the depths of the smaller frame braces B 2 equal or nearly equal to the breadth of the frame, as is often the case in larger frames, we waste material and obtain frames too heavy for the smaller locomotives. Hence, for finding the area of those portions of the upper frame braces which are marked B., in Tigs. 292, 271, and 274, we have the following rules : EULE 33a. For locomotives having cylinders 21 or 22 inches in diameter, divide the total maximum steam pressure in pounds on the piston by 2,400 ; the quotient will be the number of square inches in the cross-sectional area of the part of the frame brace marked B 2 . For locomotives having cylinders 19 or 20 inches in diameter, divide the total maximum steam pressure on the piston by 2,200. For locomotives having cylinders 18 inches or less in diameter down to 11 inches in diameter (the latter included), divide the total maximum steam pressure on the piston by 2,000 ; and for cylinders 10 inches and less in diameter, divide by 1,700; the product in each case will be the required area in square inches of the frame brace B 2 . EXAMPLE 64. What should be the cross-sectional area of the upper frame brace in a locomotive having cylinders 17 inches in diameter? Maximum steam pressure on the piston is 120 pounds per square inch. The area of a piston 17 inches in diameter is equal to 226.98 square inches ; hence, 226.98 x 120 2000 = 13.618 square inches in the sectional area of the upper frame brace. MODERN LOCOMOTIVE COXSTRrCTIoy. 193 215. When the area of the upper frame brace B 2 is known and the width of the frames established, as in Figs. 271 to 279, the depth of the upper frame brace can be readily obtained, thus: Kn.E :>4rt. Divide the area of the frame brace B 2 by the suitable width of frame given in Figs. 271 to 279. EXAMPLE (if). What should be the depth of the upper frame brace for a locomo- tive having cylinders 18 inches in diameter! Maximum steam pressure on the piston is 120 pounds per square inch. The area of a piston 18 inches in diameter is 254.47 square inches ; hence, accord- ing to Kule 33, the area of the upper frame brace must be 254.47 x 120 '(100 : 15.26+ square inches. In Fig. 271 we see that the suitable width of the frame for a locomotive with cylinders 18 inches in diameter should be 4 inches. According to Rule 34o, the depth of the brace will be 15.2(5 r = ,3.81 inches. Comparing this answer with the dimension given in Fig. 271, we find the two to agree very nearly. By the same rules the depths B. 2 of all the upper frame braces in Figs. 272 to 279 have been obtained ; and in order to avoid in these dimensions fractious of -fV inch, the depths of the upper frame braces given in some of these figures are very nearly J of an inch deeper than obtained by computation. The part of the upper frame brace marked B, which forms the top of the pedestal jaw, is generally made \ inch deeper sometimes more than the depth of that part of the upper brace marked B.,\ by so doing, the stiffness of the pedestal jaw is increased, and will to some extent prevent injury to it when the bolt D or the pedestal cap C is removed. The portion of the upper frame brace marked _Z? 3 , between the rear pedestal and the rear end of frame, in Figs. 289, 291, 292, is not subjected to such severe vertical stress as some of the other portions of the brace, and therefore the depth of that part marked /? ;t is generally made 4 inch less than the depth found by Rule ',\4/i. 216. The thickness, marked 0, of the pedestal legs in Figs. 292, 29"), and 280 is not always made alike by the different locomotive builders. Our practice has been to make the thickness o for straight pedestal legs equal to the depth of the frame brace B.,, as found by Rule 34, and for the tapered pedestal legs, the thickness o in the center of the length of the leg was also made the same depth. These dimensions of the pedestal legs have always given good satisfaction, and we believe can be safely adopted. 217. It will be noticed that when the cast-iron thimble T and the bolt D at the bottom of the pedestal, Fig. 295, are used, we are compelled to place the lower frame brace L nearer in line with the center of the driving axles than when pedestal eaps are adopted, as shown in Fig. 292 ; and therefore the lower frame brace L in Fig. 295 will be subjected to a greater pulling force than that in Fig. 292. Hence, for finding the depth of the lower frame brace L, we have the following rules : 194 MODERN LOCOMOTIVE CONSTRUCTION. BULE 35a. When east-iron thimbles at the bottom of the pedestal are used, as shown in Fig. 295, multiply the depth of the upper frame brace B 2 , as found by Eule 34a, by the decimal .86 ; the product will be the depth of the lower frame brace L. EULE 36. When pedestal caps are used, as shown in Fig. 292, multiply the depth of the upper frame brace B 2 , as found by Eule 3-ia, by the decimal .69 ; the product will be the depth of the lower frame brace L. EXAMPLE 66. What should be the depth of the lower frame brace for a locomo- tive having cylinders 18 inches in diameter, when cast-iron thimbles are to be used at the bottom of the pedestal, and the maximum steam pressure is to be 120 pounds per square inch of piston I We find in Fig. 271 that the depth of the upper frame brace B 2 , suitable for this size cylinder and steam pressure, is 3f inches ; hence we have, according to Eule 35a : 3.75 x .86 = 3.22 inches for the depth of the lower frame brace L. EXAMPLE 67. What should be the depth of the lower frame brace for a locomo- tive having cylinders 11 inches in diameter, when pedestal caps are to be used at the bottom of the pedestal, and the maximum steam pressure is to be 120 pounds per square inch of piston ? In Fig. 278 we find that the suitable depth of the upper frame brace for this size cylinder and steam pressure is 2 inches ; hence we have, according to Eule 36 : 2 x .69 = 1.38 inch for the depth of the lower frame brace L. Since the bottom surface of this brace is not planed along the entire length, that part of the same brace to which the pedestal cap is bolted is usually made to \ inch deeper than the depth found by the rule. This extra depth of the lower frame brace will restore some of the strength lost by the holes drilled for the pedestal cap bolts. THICKNESS OF THE PEDESTAL CAP. 218. The thickness C of central portion of the pedestal cap, Fig. 280, is usually made | inch less than the depth of the lower frame brace L. The projections M, Fig. 280, of the pedestal jaw generally extend into the cap of an inch for the smaller engines, and 1 inch for the larger engines ; and since the bottom of the projections u are generally in line with the top of the central portion C of the cap, it follows that the ends of the pedestal cap must be made that much thicker. The projections u are slightly tapered, so that they can be easily entered into the recesses in the cap, and when the cap is screwed fast into position they will firmly hold the ends of the pedestal jaw. NUMBER OF BOLTS IN PEDESTAL CAPS. 219. It is the general practice to secure the pedestal caps in small engines with two bolts, and in larger engines with four bolts. We believe that it is good prac- tice to use two bolts for each pedestal cap in locomotives having cylinders 14 inches and less in diameter. In larger locomotives four bolts should be used for MODERN LOCOMOTIVE CONSTRUCTION. each pedestal cap. The di- ameters of these bolts are given in Figs. 277, 278, 279, and 280. Fig. 292 represents a frame for a consolidation engine, having cylinders 20 inches in diameter, with all the pedestal legs ta- pered. Formerly nearly all frames had pedestals of this kind, but lately a great number, if not the major- ity, of frames have pedes- tals in which one leg is straight, as shown in Fig. 294. It will be noticed that all these pedestals have caps. Fig. 295 rep- resents a frame for the same class and size of en- gine in which cast-iron thimbles are used at the bottom of the pedestal jaw. We have frequently seen frames with this kind of pedestal in Mogul, ten-wheeled, and eight- wheeled engines, but have not seen them used in frames for consolidation engines. This frame has been designed for this book, and we believe it to possess advantages of its own for consolidation engines. BUILT-UP FKAMES. 220. Fig. 297 represents a frame which may be called the built-up frame, because, instead of it being forged in one piece, the same as all the frames previously shown, the lower brace L is fitted between the ped- estals and bolted to the same. This class of frames is looked upon with favor by a number of master-mechanics, and is used to a comparatively small extent. In our opinion the built-up frame is not as good as either one of the solid frames shown in Figs. 292 and 295; it lacks that simplicity ^ - ,. 196 MODERN LOCOMOTIVE CONSTRUCTION. which is so desirable and essential in a locomotive. The frame represented in Fig. 297 is one of the frames used in a number of consolidation engines having cylin- ders 20 inches in diameter. We consider this frame to be too light for engines with cylinders of this size. LIGHT FRAMES. 221. It has been found that when the depth B 2 of the upper frame brace is the same throughout, as shown in Figs. 292 and 295, and when the brace is rather light for the forces which it has to resist, fracture will take place somewhere in the neigh- borhood marked B 3 in Fig. 297, near the pedestal, and seldom midway between the pedestals. Consequently, when it is necessary to make the frames as light as possible to comply with given conditions of a railroad, or when a load must be hauled with a locomotive of minimum weight, as on elevated railroads, the weight of the frames can be reduced by making the depth B 2 less at the center of that portion of the upper frame brace which connects any two pedestals without weakening the frame. When the depth of the brace midway between the pedestals is to be reduced, then make the cross-sectional area and the depth B 3 near the pedestal equal to that found accord- ing to Rules 33a and 34a ; and for the center of the upper frame brace, reduce the depth so found in about the same proportion as shown in Fig. 297. For ordinary locomotives in which a little extra weight is not objectionable, in fact where this extra weight is often desirable, it is always best to leave the depth of the upper frame brace the same throughout, and plane the under side of the brace. By so doing an advantage will be gained which at first sight may appear trivial, but which in private locomotive shops is appreciated. We allude to the bolts which are required for bolting the mechanism to the upper frame braces. These bolts are generally made before they are actually needed in the erecting shop, and according to dimensions obtained from the drawing room. If now the upper frame braces are equal in depth throughout and planed to correct dimensions, not only will confusion, and sometimes the necessity of throwing bolts away, or often altering the lengths of bolts, be avoided, but the time lost by the workmen waiting for bolts, and the delay in getting the engine out of the erecting shop, will be prevented, which otherwise would have amounted to quite an item of loss to the proprietors. SLAB FRAMES. 222. Sometimes it is desirable, and particularly so in narrow-gauge locomotives, to obtain more room between the frames for the fire-box of the boiler than can be obtained by leaving the frames the full width throughout. In cases of this kind the the width of the upper frame brace B 2 along the side of the fire-box is reduced, as shown in Fig. 299, and the depth of the brace B. 2 increased, as shown in Fig. 298. In designing locomotives of this kind, precautions are taken to bring the bottom of fire- box within one inch from the top of the lower frame brace L, and never allow the bottom of the fire-box to extend below this brace; by so doing the lower frame brace is allowed to remain the full width of the frame, and room is also provided for the spring gear. MODEItX LOCOMOTIVE CONSTRUCTION. 197 When the upper frame brace is to be made in the form of a slab, as shown, its cross-sectional area for any given diameter of cylinder should be equal to that of the brace suitable for the same diameter of cylinder, and found according to Rule 33. The width of the slab is arbitrary, and is generally made as small as is prac- ticable in the designer's ^__^_ judgment. The least thick- II I Fly. 29<J ^ ^, 711-ss of slab that we have seen was li inches, used on a locomotive having cylinders 15 inches in di- ameter: the depth of the v, n , u Fig. 298 same brace was i inches. From the foregoing we can establish the following rule for finding the depth of the frame brace /A, when it is to be of the slab form: RULE 37. First find the cross-sectional area of the frame brace according to Rule 33rt, then divide this area by the given width of the slab ; the quotient will be the depth of the upper frame brace or slab. EXAMPLE 68. What should be the depth of the frame brace 7? 2 whose width is 1J inches for a locomotive having cylinders 14 inches in diameter ? The maximum steam pressure in the cylinder is to be 120 pounds per square inch. The area of a piston 14 inches in diameter is 153.94 square inches. Hence, accord- ing to Rule 33a, the area of the upper frame brace will be 153.94 x 120 f)OOQ ' 9.23+ square inches. According to Rule 37, the depth of this brace will be 9 23 ^? = 7.38, say 7f inches. FRONT SPLICES FOR PASSENGER LOCOMOTIVES. 223. The general design of the front splice, sometimes called the front end of the frame, depends upon the class of locomotives in which it is to be used. Fig. 290 represents the front splice for an eight-wheeled passenger locomotive. The manner of fastening the front splice to the main frame depends on the kind of pedestals adopted. The manner of fastening the splice to the frame, or, we may call it, the con- nection between the two, when pedestals with cast-iron thimbles and bolts are used, is shown in Fig. 289. In this connection the keys MM are usually placed in a position which will necessitate the drilling out a small portion of the keys so as to allow the bolts N N to pass through the frame ; this will prevent the keys M M from working out of position. In Fig. 291 is seen the manner of fastening the splice to frame when pedestals with wrought-iron caps are used. In this connection the bolts MM which fasten the T-end of the splice to the pedestal leg are liable to give trouble or break; to prevent this, great care must be taken in determining the diameters of these bolts, and to make them as large in diameter as possible without impairing the strength of the pedestal 198 MODERN LOCOMOTIVE CONSTRUCTION. leg. To determine the diameter of these bolts, we have the following rule, which is based upon observation : RULE 38. Multiply the width of the frame in inches by the decimal .32 ; the product will be the diameter of the bolt in inches for fastening the T-end of splice to pedestal leg. EXAMPLE 69. What should be the diameter of the bolts for fastening the T-end of splice to pedestal leg ? The width of frame is 4 inches. 4 x .32 = 1.28, say 1J inches. These bolts have usually conical heads, and countersunk into the pedestal leg. In the connection of splice to frame, it is also of great importance to have a sufficient number of bolts N N to hold the end of the frame to splice. The diameter of these bolts should be equal to about J of the width of the frame, and the shearing stress should not exceed 3,000 pounds per square inch. Assuming as before, for the sake of simplicity, that the total pulling force is equal to the total steam pressure on the piston, we can use, for determining the number of bolts through frame and splice, the following rule : RULE 39. Divide the total steam pressure on the piston hi pounds by 6,000 ; the quotient will be the total cross-sectional area of all the bolts ; divide this quotient or total cross-sectional area by the cross-sectional area of one bolt ; the quotient will be the number of bolts required through the end of frame and splice. NOTE. The reason for dividing the total steam pressure on piston by 6,000 instead of 3,000 is, that some of these bolts, frequently all, are subjected to a double shear ; that is to say, they must be sheared off in two places before the frames can be pulled apart. EXAMPLE 70. What should be the number of bolts marked N N in Fig. 289, passing through the end of frame and splice, for a locomotive having cylinders 18 inches in diameter, maximum steam pressure in cylinder 120 pounds per square inch I The diameter of each bolt to be equal to J the width of the frame. In Fig. 271 we see that the suitable width of frame for a locomotive having cylinders 18 inches in diameter is 4 inches ; hence the diameter of each bolt must be 1 inch. The cross-sectional area of a bolt 1 inch in diameter is .7854 of a square inch. The area of a piston 18 inches in diameter is 254.47 square inches ; hence, accord- 254.47 x 120 ing to Rule 39, we have, -- (\rjfv\ " = 5-089 square inches = total cross-sectional 5.089 area of all the bolts ; and 7Q ~ ( = 6.4+ say 7 = the number of bolts required. If the connection of frame and splice is similar to that shown in Fig. 289, and the number of bolts found according to Rule 39, and also assuming that the total pulling force is equal to total steam pressure on the piston, the shearing stress per square inch of cross-sectional area of the bolts will appear to be greater than 3,000 pounds, because four of the bolts N N are subjected to a shear in one place only ; but the keys M M will reduce the shearing stress to less than 3,000 pounds per square inch on the bolts, so that the foregoing rule can be safely applied in designs of this kind. EXAMPLE 71. What should be the number of bolts N N, Fig. 291, passing through MODERN LOCOMOTIVE CONSTRUCTION. 199 the end of the frame and splice for a locomotive having cylinders 14 inches in diameter, tlif diameter of each bolt is to be equal to J of the width of the frame? The maxi- mum steam pressure in cylinder is 120 pounds per square inch. In Fig. 275 we see that the suitable width of frame for a cylinder 14 inches in 3jf diameter is 3 $ inches, consequently the diameter of each bolt N N must be -j = -f$ inch. The area of a piston 14 inches in diameter is 153.94 square inches; hence, according to Rule 39, we have, 153.94 x 120 - = 3.0788 square inches for the total cross-sectional area of all the bolts. The area of a bolt if inch in diameter is equal to .69 of a square inch, and 3.0788 .69 = 4.4+ say 5 bolts. 224. The recess marked 72, Fig. 290, near the front end of the frame splice, is for the purpose of receiving the cylinder saddle, which generally butts against the rear end of the recess. The cylinder saddle is bolted to the front splice, as shown in Fig. 12, page 21, by bolts running in a horizontal direction through the flange of saddle and splice, and also by the vertical bolts B. In order to provide further security and pre- vent the cylinder from moving in a longitudinal direction that is, the direction in which acts the greatest force which the cylinders have to resist a key D is driven be- tween the front face of the cylinder saddle and end of recess. Occasionally we find master-mechanics using two keys in each frame, one at the front face of saddle and another one at the rear face. We prefer to use only one key at the front ; and believe this to be the best practice, because two frames (sometimes four) are usually slotted at one time, and consequently the distances in the frames between the pedestals and recesses will be exactly alike ; the facing strips on the cylinder saddles are planed in line and square with the axis of cylinders, and therefore by placing the cylinder saddle directly against the rear ends of the recesses, the cylinders are brought in the true position with less labor than when two keys are used in each frame. '!'!'>. In passenger engines, the lifting-shaft bearing and rocker-box, besides other mechanism, are bolted to the front splice, consequently it is subjected to the action of vertical forces of considerable magnitude, and it has also to resist the pulling force due to the pressure on one piston ; therefore in this class of locomotives it is generally made somewhat deeper than the upper frame brace B 2 in Fig. 289, but uniformity in the proportion of these depths does not exist. As a result of observa- tion on this point, we believe that the following rule will give a depth for the front splice which will agree with good modern practice. RULE 40. Multiply the depth of the upper frame brace #>, Fig. 289, by 1.15 ; the product will be the depth of the front splice. According to this rale the depth of the front splice is 15 per cent, deeper than that of the upper frame brace. NOTE. When the maximum steam pressure on the piston is 120 pounds per square inch, then take the depth of the upper frame brace B., from a pedestal, suitable for the given diameter of cylinder, shown in the group Figs. 271 to l27!>. 200 MODEEN LOCOMOTITE CONSTRUCTION. When the maximum pressure is more or less than 120 pounds per square inch of piston, then find the depth of the upper frame brace B 2 by Eules 33 and 34a. EXAMPLE 71a. What should be the depth of the front splice for a locomotive having cylinders 18 inches in diameter? Maximum steam pressure on pistons is 120 pounds per square inch. In Fig. 271 we see that the depth of the upper frame brace B., for an 18-inch cylinder is 3| inches ; hence, according to Rule 40, we have, 3.75 x 1.15 = 4.3125 inches, which is the depth of the front splice. The depth of the front splice at the recess should be equal to the depth of that portion of the upper frame brace which is marked B 2 (see Fig. 289), and the depth of the splice from the cylinders to the bump- ers should be equal to the depth B%. 226. The front end P of the splice is often turned down, forming an off- set, as shown in Fig. 290. To this offset is bolted the bumper, usually made of wood. In some locomotives the offset at P is in an upward direc- tion, so as to bring the bumper to a suitable height above the rails for con- venience in coupling to the cars. In cases of accidents or collision, the front end P of the splice is very liable to be broken off or otherwise injured, and to repair the damage the whole splice will have to be taken off. To obviate this difficulty and thus save considerable time and labor, many master-mechanics now make the splice perfectly straight at the front end, and in place of the offset P use a cast- ing, of which an elevation and plan are shown in Figs. 300 and 301. This cast- ing here shown is suitable for loco- motives having cylinders 17 inches in diameter ; for smaller engines the dimensions may be somewhat decreased, and for larger ones they should be increased. 227. Figs. 293 and 296 represent the front splices for consolidation engines, and a similar form of splice is also often used for Mogul engines. These splices pass over the top of cylinder saddle, and are fastened by bolts D I), Figs. 292 and 295, passing through the front splice, cylinder saddle, and front end of main frame ; they are also fastened to the main frame by the bolts N N, and further secured in position by the keys R 7?, and also by the keys K K between the cylinder saddle and end of recess in the splice. MODEBX LOCOMOTIVE CONSTRUCTION. 201 DEPTH OF FRAME SPLICES FOR MOGUL AND CONSOLIDATION ENGINES. 228. When the form of the splice is like that shown in Fig. 295, the depth of that part of the splice marked S between the main frame and saddle, and also that portion of the splice which lies on top of cylinder saddle, should be equal to that of the upper frame brace marked It.,. The depth of the splice in front of the cylinder saddle can be made equal to that of the upper frame brace which is marked B 3 . FRONT SPLICE AND MAIN FRAME FORGED IN ONE PIECE. 229. Sometimes the front splice and main frame are forged in one piece, as shown in Fig. 302. This we consider to be very bad practice, because, should the front end Fig. 303 be injured, the whole frame will have to be taken down to repair the damage, which will involve a great amount of unnecessary labor and expense. FRAME BOLTS. 230. The bolts which are used for bolting the different parts of the engine to the frames are, by the majority of locomotive builders, made straight, accurately turned to fit reamed holes, and driven home. Other builders make these bolts tapered, generally i inch to the foot that is, in the length of one foot the diameter is increased | inch and turn them to such dimensions as will allow the bolts to enter the reamed holes to within J of an inch from the head of the bolt ; through this distance of i inch the bolts are driven home. We are inclined to believe that the use of tapered bolts is the best practice, as when these bolts become slack, then by turning a small amount off the under side of head, the bolts can again be driven tightly into the holes. We also believe that tapered bolts will hold the parts more firmly together than straight bolts. Bolts which are very long, as those marked I) /> in Figs. 2!>l> and 295, should always be tapered, which we believe to be the best practice. SI 'I, 'ING SADDLES. 231. Fig. 303 represents the pedestal /', with driving axle box /?, wodire.x IT W 2 , and spring saddle .V in position. A portion of the spring /and also the spring strap H are shown. Fig. 304 represents a vertical section through the centers of the same 202 MODERN LOCOMOTIVE CONSTRUCTION. mechanism. Spring saddles of the form here shown are made of cast-iron, and are suitable for locomotives having cylinders larger than 12 inches in diameter. The base E E of these saddles is made as wide as the space between the wedges will permit, leaving a sufficient amount of metal around the recesses in top of the driving box in which the base of the saddle is placed. Pai't of the metal at F, in the base E E of the Jfty. SOS i -W- Fio-\30G Fig. 307 ffroiiffltt Iron Saddle saddle, is cut out, thereby giving access for oiling the axle journal. A saddle with this kind of base will have a firmer support than, and is not so liable to upset, as a saddle with a narrow base, similar in form to that shown in Fig. 306. The width of the spring saddle is made to allow at least J inch clearance at each side of the frame, as shown in Fig. 304. A recess is cast in the top of the saddle to receive the spring strap H. At the center, in the bottom of the recess, a fulcrum G is cast to fit into a groove cut in the bottom of the spring strap H, the whole arrange- ment being such as will allow the spring I to rock through a short distance. 232. Some locomotive builders do not cast the fulcrum G in the recess, but make the bottom of it perfectly flat, as shown in Fig. 305. In this recess a piece of rub- ber E is placed, with a wrought-iron plate P on top. This plate is about i inch thicker in the center than at the ends, so that when the spring strap (in this case without a groove cut in it) is placed on top of the plate, the spring can rock the required amount. In this kind of spring saddle the recess should always be deep enough to allow the spring strap to enter it at least J inch, to prevent the spring from moving out of position. 233. Sometimes the spring saddles are made of wrought-iron, their form being similar to that of the cast-iron ones, with the exception of the recess, which is left off. The tops are straight, and a pin A, as shown in Fig. 306, screwed into the top. This pin is made to fit loosely in a hole in the bottom of the spring strap, and prevents the spring from moving out of position. The bottom of the strap is made convex, to allow the spring to rock. MODERN LOCOMOTIVE CONSTRUCTION. 203 Occasionally, when wrouglit-iron spring saddles are used, a roller is inserted between the saddle and strap, lying in suitable grooves cut into both. The roller has also collars at each end, to prevent the spring from slipping sideways. For locomotives having cylinders 12 inches in diameter and less, the straps are made of wrought-iron, of a form as shown in Figs. 306 and 307, which need no further explanation. DRIVING AXLE BOXES. 234. The play or clearance between the axle box and hub of driving wheel F, Fig. 304, is generally ?- 6 inch, and the clearance between the axle box and collar U is equal to the same amount, giving the driving axle a total amount of inch play or movement in the direction of its length. Occasionally we find driving axle boxes in which the distance K (Fig. 304), that is, the distance from the center line X Y to the outside face of box, is less than the distance L from the center line X Y to the inner face of box, the difference generally Fig. 313 being J to ,-% inch. The object of this difference is for the purpose of turning the axle box around to take up the wear between it and the face of wheel, when that becomes excessive. 235. Driving axle boxes, or which, for the sake of brevity, are often called driving boxes, consist essentially of three parts, namely, the casting marked A A in Fig. 308, an oil cellar C, and the brass B. The driving boxes may be divided into two classes, the form of the brass B being the distinguishing feature. Figs. 308, 309, 310 represent different views of one class of driving boxes, in 204 MODERN LOCOMOTIVE CONSTRUCTION. which the octagonal fonn of brasses are used, and Figs. 311, 312, 313 represent the other class of driving boxes, in which the cylindrical form of brasses are used. Occasionally we find the casting A A made of brass; in such cases a separate brass bearing is not used ; but boxes of this kind are seldom adopted, and therefore we will confine our attention to that class of boxes which are called cast-iron driving boxes. In proportioning these boxes great care must be taken to 'have the depth f/f of the lug A 2 , Fig. 311, sufficiently great so that it cannot be broken off by pressing the brass into the box, or the strength of the lug A 2 impaired, causing it to break off when the engine is running. In large driving boxes the depth g f should be at least 1J inches. In a great number of locomotives the inner faces of the flanges m m, Fig. 312, are planed parallel to each other, and in a small number of engines the inner surfaces of these flanges are planed to a form, as shown in Fig. 313; that is, when planed the flanges are about -^ inch thicker in the center p than at the ends o o. The object of this form of driving-box flange is to prevent the same from binding against the pedestal wedge, and at the same time give the box a greater freedom to adjust itself to the journal when one end of the axle stands higher than the other end, caused by running over an uneven track. The width I I of. the flanges, Fig. 312, should be sufficient to allow their lower ends, when the box is in the lowest position in the pedestal, to cover the pedestal legs. By this arrangement the lateral stress on the flanges of the wedges will be less than when the driving-box flanges do not reach the pedestal legs. 236. The oil cellar (7, Fig. 311, is made of cast-iron, and its purpose is to hold the waste, tallow, and oil to lubricate the journal. The ends of the cellar are planed to fit accurately in the box ; and it is held in the box by two bolts r r, which are roughly turned and fit in the holes somewhat loosely ; these bolts are secured in position by means of the split keys s. In many driving boxes the end surfaces u u of the cellar are pai'allel to each other ; in others we find these surfaces inclined towards the cen- ter, making the width at the top of the cellar about inch less than at the bottom. The reason for tapering the width of the cellar is, that it must be removed before the driving box can be taken off the axle; but experience has shown that the lower ends of the driving box will close after it has been in use for some time, and clasp the oil cellar very tightly, and therefore a tapered oil cellar can be more readily removed when it is necessary to do so than one with parallel ends. 237. The pockets n , Figs. 311 and 312, in the top of the driving box, receive the ends of the spring saddle and prevent the latter from moving out of position. The recesses k k are for the purpose of leading all the oil which may be poured on the top of the box into the oil holes i i. DRIVING-BOX BRASSES. 238. There are some objections to the use of octagonal brasses ; for instance, they require a considerable amount of labor to fit them in the box as accurately as they should be ; and again, since the ends of these brasses are not firmly secured in the box, they are liable to close, press against the axle journal, and consequently become MonKii\ LocoMOTirs coxsTnrcTiny. 205 hot in a very short time, and for these reasons the octagonal form of brass is not extensively used. The eylindrieal form of brass shown in Fig. 311 gives better satisfaction, and is the form adopted in a large majority of locomotives. Its outer surface is accurately turned, the casting A A is slotted, and the brass pressed in with a pressure of about five to seven tons. The edge d of all driving-box brasses generally extends i to f inch below the center of the axle; and the edge g generally extends inch below the edge d; the object of this form is to hold the ends securely in position, so as to prevent them from closing, and thereby avoid hot journals. Even when these brasses are accurately fitted and pressed in the box very tightly, they will in time become loose, and will have to be replaced. In order to make these brasses remain tight in the box for a greater period of time, some master-mechanics will drive two brass pins t t, about f inch in diameter, through each side of the box and brass. These pins are, for obvious reasons, driven at an angle with the sides of the box, as shown in Fig. 311. Another advantage gained by these pins is that, when collars on the driving axle are not used, as is sometimes the case, the brasses, when they have become loose, cannot slip out of the box. In the top of the brass is cast an oil groove h, about inch square. This groove extends to within 1 inch from the ends of the brass. The oil is led into this groove by two oil holes i i, each about inch in diameter. Babbitt metal is used in many driving-box brasses. Grooves, about J to 1 inch in width, and extending sometimes the whole length of the brass, and at other times to about 3 inch from the end of the same, are cast into and near the top of the brass, as indicated by </ <j in Figs. 308 and 310. We believe that the Babbitt metal in driving-box brasses is worse than useless, because the waste in the oil cellars will accomplish the same purpose for which Babbitt metal is intended, namely, to prevent the dust from spreading around the axle journal. Besides, in our experience, we have found that, since the pressure of the brass against the journal is very great and acting constantly, and since the Babbitt metal will collect and hold the dust, the axle journal will wear comparatively very rapidly, and for these reasons the brass is better without it. PROPORTIONS OF DRIVING AXLE BOXES. 239. In designing a locomotive driving box we must not lose sight of the fact that all the weight which is placed upon it must be supported by the upper part of the axle journal. Indeed, herein lies a great difference between a locomotive driving box and an ordinary pillow block similar to those used in many stationary engines. In the for- mer the pressure is against the upper part of the box, and consequently the oil which is fed through the oil holes in the top of the box will be aided to flow away from the elements of contact. In the ordinary pillow block the pressure is against its lower part, and if the pressure is not sufficiently intense to force out the lubricant from between the surfaces, the oil will be aided to some extent to flow towards the element of contact. It must also be remembered that the vertical pressure on a locomotive axle journal 206 MODERN LOCOMOTIVE CONSTRUCTION. is almost constant, which will in nowise assist in the lubrication of the journal. In pillow blocks of stationary engines, although the pressure is generally towards the bot- tom of the block, it will shift a little from one side of the pillow block to the other as the piston changes the direction of its motion, and thereby assist in the lubrication of the journal. These considerations lead us to conclude that locomotive axle journals are more liable to become hot than the main journals of stationary engines. To prevent as much as possible hot axle journals, we must proportion them in a manner which will allow upon them a comparatively low pressure per square inch. The pressure on any journal is estimated by the pressure per square inch of its projected area. By the pro- jected area is meant the area of a rectangle whose length and breadth are respectively equal to the length and diameter of the journal. 240. The pressure on an axle due to the weight of the engine is not the only press- ure which the axle journal has to resist ; it has also to resist a pressure due to the load which the engine has to haul. The latter pressure is not a constant quantity, but the ratio between the pressure due to the weight of the engine and that due to the maxi- mum load is about the same in all engines ; and therefore, for the sake of simplicity, we may leave the pressure due to load out of the question, and proportion the journal according to the pressure due to the weight of the engine. Close observation and experience in modern locomotive construction lead us to be- lieve that a pressure of about 160 and not ovev 175 pounds per square inch of projected area, due to the weight of the engine, agrees with the best modern practice and may be adopted ; the former figure, namely, 160 pounds per square inch, should be preferred ; it will give the best results. 241. From the foregoing it will be seen that, in order to design the driving box, we must first determine the total weight which the driving axle journals will have to support. The weight on the driving axle journals for new locomotives can generally be esti- mated only approximately, because the design is not sufficiently advanced to obtain the exact weights of the different parts of the engine and running gear ; yet experience will enable us to estimate this weight close enough for all practical purposes. In Art. 24, tables will be found which give the weights on drivers in the various classes of locomotives. Table 5 contains the weights on drivers in eight- wheeled passenger en- gines, to which we shall refer here. Now, in order to determine the weight which the driving axle journals in eight-wheeled passenger engines will have to support, we must subtract the sum of the weights of the wheel centers, tires, axles, side rod, etc., in fact, the weight of all pieces which are supported directly by the track, from the total weight on drivers given in Table 5 ; one-fourth of the remainder will be the weight on each journal. If the design of the engine is not sufficiently advanced to obtain the accurate weights of the driving wheels, axles, side rods, etc., we can generally estimate the sum of these weights by assuming them to be from to \ of the total weight on the drivers. Thus, let it be required to find the weight on the driving axle journals for an eight- wheeled passenger engine having cylinders 16 inches in diameter. In Table 5 we find the total weight on the drivers for a locomotive of this size to be 47,665 pounds. One- MODERN LOCOMOTirE CONSTRUCTION. I I Kl L X A KS ^ 1 " I " I ^--4-^-r 208 MODERN LOCOMOTIVE CONSTRUCTION. fourth of this weight will be the estimated sum of the weights of the parts supported 47665 directly by the track. Hence, 47665 - weight supported by all the driving axle journals; and = 35749 pounds, which is the total 35749 = 8937 pounds sup- ( as f~~ t ~' ported by each driving axle journal ; or, we may say that the pressure on the projected area of the journal is 8,937 pounds ; and since the pressure per square inch is to be about 160 pounds and not exceed 175 pounds, we must proportion the diameter and length of the journal accordingly. By the term " length of journal " we mean that length which is equal to the width A (Fig. 316) of the driving box, and neglecting the short length of journal required for the play between the axle box and hub of driving wheel. 242. When the driving axle is made large enough to prevent heating, and, to fulfill conditions peculiar to the locomotive, also properly fitted into the hub of the wheel, we have generally an axle strong enough to resist all the forces which may act upon it, and therefore in determining the diameter and length of journal w r e may throw out of considera- tion the strength of an axle. One of the conditions peculiar to the locomotive, and to which a driving axle must conform, is the width A of the axle box (Fig. 316), which is short when compared with the lengths of pillow blocks in stationary or marine engines. This width A of the axle box is limited by the distance between the cylin- ders and also by the gauge of the track ; the latter is established, and therefore if we make the axle box too wide, then, since the center of the width of frame and the center of axle box should. coincide, or very nearly so, we must either move the frames closer together to a corresponding amount, and thus be compelled to reduce the width of the fire-box, which is decidedly an objectionable feature, or we must increase the distance between the cylinders, which is also objectionable. The width A of the axle box should be only suf- ficient to allow for the proper thickness of the flanges on the box and wedges to give these the requisite strength. Figs. 314 to 340 represent driving boxes suit- able for the pedestals shown in Figs. 271 to 279, LOCOMOTIVE COXSTRTCTION. 209 and are designed for eight-wheeled passenger locomotives of various sizes, includ- ing those having cylinders 10 inches in diameter, and -up to 18 inches in diam- eter. The given dimensions of these boxes agree with the average modern loco- motive practice. From those illustrations we can readily obtain the width of the boxes, and all the main dimensions. The part shown in section at the right-hand side of all the plans of the boxes, such as Figs. 316, 319, 322, etc., and marked W in some of them, represent a section of the long wedge; the distance between the flanges of the wedges is the thickness of the frame, and this thickness subtracted from the distance between tlje flanges of the boxes and divided by two will give the thick- ness of each flange on the wedge. J4:>. Having established the width of the driving boxes, the diameter of the journal is easily obtained by the following rule : RULE 41. Divide the weight on the journal by 160 ; the product will be the num- ber of square inches in the projected area ; divide this quotient by the width A (Figs. 316 to 340) of the driving box in inches; the quotient will be the diameter of the journal in inches. EXAMPLE 72. What should be the diameter of a driving axle journal for an eight- wheeled passenger engine having cylinders 16 inches in diameter ? We have already seen in Art. 241 that the total pressure on the projected area of one driving axle journal for this class and size of engine is 8,937 pounds. In Fig. 322 we find that the width of box should be 8 inches. Hence to find the diameter we 8937 have, according to Eule 41, -rr = 55.8, which is the number of square inches in the K.r. o projected area, and ^~ = 6.97 inches = diameter of the journal. If we make the diameter of this axle equal to that given in Fig. 320, namely, 6J inches, the pressure per square inch on the projected area will be 165.5 pounds, providing our estimated weight of wheels, tires, axles, etc., is exactly correct. EXAMPLE 73. Find the diameter of a driving axle suitable for an eight-wheeled passenger engine whose cylinders are 12 inches in diameter. In Table 5 we find the total weight on the drivers to be 29,700 pounds. Allowing | of the total weight on the drivers for the mechanism whose weight is not supported 29700 by the journals, we have, 29700 - - = 23760 pounds pressure on all the four o 23760 journals and ~r~ = 5940 pounds pressure on the projected area of each journal. 5940 Again, = 37.12 square inches in each projected area. In Fig. 334 we find that for a passenger locomotive with cylinders 12 inches in diameter, the width of the driving box should be 6f inches, and consequently the diameter of the journal 37 12 should be fi '- = 5.49 inches. These dimensions agree with those given in the illustrations. From the foregoing it will bo seen that in determining the dimensions of a locomo- tive driving axle journal, we have followed the law of simple proportionality of friction 210 MODERN LOCOMOTIVE CONSTRUCTION. to pressure. In relation to this law, Prof. W. J. M. Rankine says: The law of simple proportionality of friction to pressure is only true for dry surfaces, when the pressure is not sufficiently intense to indent or grind the surfaces ; and for greased surfaces, when the pressure is not sufficiently intense to force out the unguent from between the surfaces where it is held by capillary attraction. If the proper limit of intensity of pressure be exceeded, the friction increases more rapidly than in the simple ratio of the pressure. That limit diminishes as the velocity of rubbing inci*eases, according to some law not yet exactly determined. The following are some of its values, deduced from experience : RAILWAY CARRIAGE AXLES. Limit of pressure per square inch. Velocity of rubbing surface, 1 foot per second 392 " " " 2i feet " " 224 " " g " tt i AQ The limit of the pressure on journals given by Professor Rankine is exceeded on the journals proportioned by the foregoing rules, and such as are used in modern locomotives, yet these journals are giving good results, and seem to be suitable for the purpose intended. But if the average speed of the present locomotive is to be increased, so that the velocity of the circumference of the journal exceeds 9 feet per second, the lengths of these journals may also have to be increased, so as to reduce the pressure per square inch to considerably less than 160 pounds, even if we are com- pelled to increase the distance between the cylinders. 244. The driving boxes shown in Figs. 314 to 340 were proportioned to suit one particular class of locomotives, namely, eight-wheeled passenger engines. From our remarks in Art. 243 it will be seen that the size of a box for a passenger engine depends upon the weight on the drivers ; and since the cylinders are proportioned in accord- ance with the weight on the drivers, we may assume and say, as our illustrations indicate, that the size of a box depends upon the diameter of the cylinder used. In Mogul, ten-wheeled, and consolidation engines the diameter of cylinder is also propor- tioned in accordance with the weight on drivers ; but under any one of these engines there are more driving wheels than under an eight-wheeled passenger engine, and consequently the size of the axle box suitable for an eight-wheeled passenger engine, with cylinders of given diameter, may or may not be suitable for a Mogul, ten- wheeled, or consolidation engine having cylinders whose dimensions are equal to those of the cylinders in the passenger engine. It therefore remains for us to consider the con- ditions which influence the size of the journal in these engines, thereby enabling iis to determine its dimensions and select the proper size of driving box, from the number shown in Figs. 314 to 340. In Mogul, ten-wheeled, and consolidation engines, as well as in passenger engines, the weight on the journals must be distributed in such a manner as to prevent heating; and the rules given for finding the dimen- sions of the driving axle journal for a passenger engine may also, with a slight change, namely, less pressure per square inch on the projected area of the journal, be used for computing the dimensions of driving axle journals in the other classes of engines. MODEKX LOCOMOTirE COXSTRCCTIOX. 211 From the foregoing we perceive that in all locomotives the driving axle journals are proportioned to the pressure due to the weight on the driving wheels, and when this is correctly done, sufficient allowance will then have been made for the pressure due to the load which the engine has to haul ; we therefore leave the load to be hauled out of consideration in the calculations. In determining the sizes of journals for Mogul, ten-wheeled, and consolidation engines, we must not lose sight of the fact that, in these classes of engines, particularly in Mogul and consolidation locomotives, the driving wheels are smaller in diameter than those in eight-wheeled passenger engines, and consequently the axles are brought closer to the track and exposed more to the dust, thereby raising conditions favorable for cutting the journals. Again, it often happens that, on the road, the counterbalance weights are in the way of oiling the journals, and therefore, if the time is limited, it may happen that the oiling of some of the journals will be neglected. These classes of locomotives are also more or less looked upon as freight engines, and do not always receive the same care as bestowed upon passenger engines. For these reasons it is always advisable to make the journals for freight engines comparatively large in diameter. We therefore recom- mend that their driving axle journals shall be so proportioned as not to allow more than 160 pounds per square inch on the projected area of the journal ; in fact, 160 pounds should be the limit, instead of 175 pounds, as given for passenger engines, and when the design or other given conditions will allow, the pressure per square inch should be even less than 160 pounds. The dimensions of driving axle journals in the following tables are recommended. The pressure per square inch on the projected area of these journals will be less than 160 pounds, when the weight of the engines correspond to the weights given in Tables 5, 6, 7, and 8 : TABLE 17. DIMENSIONS OF DRIVING AXLE JOURNALS FOR MOGUL ENGINES. Diameter of Cylinders. Diameter of Journal*. Length of Journals. 11 inches. 5 inches. 6 inches. 12 " 5i 6f " 13 " 5i 71 " 14 " 6 7f " 15 " <H 7f " 16 " 6f 8 " 17 " 6f 8 " 18 " 7* 8 " 19 " 8 9 " TABLE 18. DIMENSIONS OF DRIVING AXLE JOURNALS FOR TEN-WHEELED LOCOMOTIVES. Diameter of Cylinders. Diameter of Journal*. Length of Journals. \- inches. 5 inches. 6J inches. 13 " 5i " 6} " 14 " 6 " 7J " 1f> " 6 75. 16 " 6* 7J 17 " 6} 8 1H " 7i 8 " 19 " 8 9 " 212 MODERN LOCOMOTIVE CONSTRUCTION. TABLE 19. DIMENSIONS OF DEIVING AXLE JOURNALS FOR CONSOLIDATION LOCOMOTIVES. Diameter of Cylinders. Diameter of Journals. Length of Journals. 14 inches. 15 " 20 " 24 " 5 inches. 5* " 74 " 8 " 6i inches. 7f " 8 " 9 " 245. Although there are many locomotives with cylinders of the same diameters as given in these tables running with smaller journals, yet the dimensions given in the tables agree with the average sizes of journals in modern locomotives. For the sake of comparison, we append Table 20, in which are given the dimen- sions of a few driving axle journals in modern locomotives doing excellent service : TABLE 20. Class of Locomotive. Dimensions of Cylinders. Diameter of Driving Axle Journal. Diameter of Main Driv- ing Axle Journal. Length of Journals. 17" x 24" 1\ inches. 7J inches. 8 inches. 18" x 24" 8 8 gi a it n 18" x 24" g 8 12* 18" x 24" 71 7| 8 18" x 24" 74 74 8 it n 19" x 24" 7i 7$ 8 20" x 24" 74, 74 8 In Table 20 it will be seen that in some of the locomotives the journals of the main driving axle that is, the axle to which the connecting-rods are attached are made \ inch larger in diameter than the other driving axle journals. Although this is good practice, there are master-mechanics who object to such an arrangement, because it compels them to keep, for each class of engine, two sizes of driving boxes on hand ready to replace worn-out ones, thereby increasing the stock which must be kept to facilitate quick repairs. The dimensions of the driving axle journals given in Tables 17, 18, and 19 also establish the sizes of driving boxes ; and consequently we have only to select, from the number of boxes shown in Figs. 314 to 340, that box which will fit the journal to be used. When the right driving box has been selected, we then select the correspond- ing pedestal from the number of pedestals shown in Figs. 271 to 279. It should be remembered that the dimensions of the upper braces JB 2 , and the lower braces L, uniting the pedestals, must be computed to suit the diameters of the cylinders; and therefore in frames for freight engines the braces uniting the pedestals will be heavier than those shown in the illustrations. To make this plain, we will take an example. Let it be required to find the principal dimensions of a frame for a consolidation engine with cylinders 20 inches in diameter. In Table 19 we see that the driving axle journal must be 7 inches diameter and 8 inches long, hence the MODERN LOCOMOTITE CONSTRUCTION. 213 box to be used is that one which is represented in Fig. 317 ; and the pedestal to be used for tliis box is represented in Fig. 272. But now, the dimensions for the upper and lower frame braces must be determined according to Rules 33a, 35, and 36, to suit a cylinder 20 inches in diameter, and consequently these braces will IH- heavier than shown in Fig. 272, but the dimensions of the pedestal itself will remain as they are given. There are also a few eases in which the choice of the axle box will either compel us to change the width of frame suitable for a given diameter of cylinder as established in the illustration of pedestals, or we must increase the width of the axle box to suit the given width of frame. CHAPTER VI. DRIVING AXLES. DRIVING WHEELS. COUNTERBALANCE. DRIVING AXLES. 246. The driving axles are made of iron or steel ; the wi'iter prefers good ham- mered-iron axles. Some of the different forms of driving axles, such as are generally adopted under all classes of locomotives, are shown in Figs. 341, 342, and 343. Fig. 341 represents a main driving axle suitable for eight-wheeled passenger locomotives, with cylinders 16 inches in diameter ; a Mogul engine with cylinders 16 inches in diameter ; or a ten- wheeled locomotive with cylinders 17 inches in diameter. Those parts of the axles marked A A are generally called the wheel fits, and are usually turned to inch less in diameter than the journals of the axles marked B B ; in fact, in this style of axles the difference between the diameter of the wheel fit and that of the journal should never be greater than J inch, as this will give a shoulder sufficient for all practical purposes ; on the other hand, if the difference between these diameters is greater than inch, the axle will be unnecessarily weak- ened, and will be liable to break off at the hub of the wheel. Sharp 'corners at // are another cause which will lead to the breaking of the axles near the hub, and therefore sharp corners should not be tolerated; the junction between the wheel fit and the journal should always be a curve. Although this manner of forming the wheel fit A, that is, turning it to a smaller diameter than that of the journal, is quite a common practice, we believe it to be inferior to that shown in Fig. 344. In this design the diameter of the wheel fit is equal to that of the journal, and consequently the strength of the axle is in nowise impaired. The shoulder against which the hub of the wheel is pressed is formed in turning by leaving on the axle a small collar H, about -$ inch larger in diameter than the journal, the thickness of this collar being about | inch at the top. Here, also, sharp corners at i i must be avoided, and the junction between the collar and axle nicely rounded out. The hub of the wheel is counterbored to receive the collar, as shown in the illustration. This design of an axle has an advantage over those shown in Figs. 341, 342, and 343, namely, in axles with wheel fits like that shown in Fig. 344 ; the journal can be trued up when necessary and still leave the shoulder H unimpaired. 247. Sometimes we find the main axles turned to equal diameters from hub to hub of wheels, and frequently we find them formed as shown in Fig. 341. In MOVERS LOCOMOTIVE COSSTBUCTIOX. 215 the latter axle the central part C is left smooth forged; the parts B B are made sufficiently long to receive the axle box and eccentrics. Fig. ;>4L' represents the rear driving axle of an eight-wheeled passenger engine with cylinders 1G inches in diameter. The same size and form of axle is also used * a under other engines under which a main axle like that in Fig. 341 is used. In these driving axles the central part C and the projections which form the shoulders are left smooth forged; the amount of projection is equal to amount of metal allowed for turning the journals B. The cast-iron collars G G are either shrunk on the axle, or held in position by two set screws. Oc- casionally we find the driving axle made as shown in Fin 'III Fig. 343. The only difference between the axle shown in Fig. 342 and that in Fig. 343 will be found in the form of the central part CC; in the latter the diameter is gradually reduced from the collar to the center ; and in the former it is of equal diameter throughout. DRIVING WHEELS. 248. Fig. 345 represents the front view, Figs. 346, 347, sections of a driving wheel, and Figs. 348, 349 represent sections of its arms. This wheel was designed for and is successfully used under eight-wheeled fast passenger engines with cylinders 18 inches in diameter. A driving wheel consists of two parts, namely, the driving wheel center marked C, and the tire marked T. In this country the driving wheel centers are made, almost universally, of cast-iron. Sometimes the spokes are cast solid, but usually they and the rim are east hollow. The crank N and the counterbalance form part of the wheel center. The most common practice in fastening the tires on the wheel center is to shrink them on the center. To do this, the wheel centers are turned square across (not 216 MODERN LOCOMOTIVE CONSTRUCTION. MI>IH:I;\ < <>\sri;r<"ri<>\. 217 tapered), and the tire bored out somewhat smaller in diameter than that of the wheel enter. The tire is then heated, generally on account of cleanliness, by means of a number of gas (lames arranged for the purpose. When the tire, by these means, has l>een sufficiently expanded, it is then slipped on the wheel center and allowed to cool, thereby contracting and binding it firmly around the cast-iron center. TABLE 21. STANDARD SIZES OF WHEEL CENTERS. Diameter of Wh<,>el Centers. Inside Diameters of Tires. 38 inches. 44 50 56 62 66 38 inches, less 0.040 44 ' " 0.047 50 ' " 0.053 56 ' " 0.060 62 ' " 0.066 66 ' " 0.070 A uniformity in the diameters of wheel centers has not yet been thoroughly established. In 1886 the American Railway Master Mechanics' Association recom- mended and adopted the above di- ameters as standards. In this table we see that, for the given diameters of wheel cen- ters, the shrinkage allowance in the bore of the tires is 0.040, 0.047, 0.053, 0.060, 0.066, and 0.070 of an inch respectively, and these are claimed to be the average of the wide range of shrinkage allowance used in actual practice. 249. Figs. 350, 351, and 352 represent the different views of a driving wheel designed for a ten- wheeled engine having cylinders 19 inches in diameter ; Fig. 353 rep- resents the sections of the spokes. In this wheel the spokes are solid and the rim is cast hol- low, with the exception of that part which forms the counter- balance 000, extending from u (Fig. 250) to an equal distance on the other side of the center line; this part of the rim is cast solid. Fig. 353 Fig. 351 Fig. 352 In order to avoid a shrinkage stress, the counterbalance is parted at s s; these open- ings extend to the rim, but not through it; the latter is parted or cored through 218 MODERN LOCOMOTIVE CONSTRUCTION. at r and in a corresponding place on the other side of the center line. The openings r are generally slotted and cast-iron liners driven in. In this wheel the whole crank is cored out, the cored part extending to the axle, and leaving all around it an opening 1| inches wide. There is an objection to this opening : it will interfere with the guidance of the axle when it is to be pressed into the hub of the wheel. It seems to us that a few ribs cast into the core opening around the axle will be an improvement, by which considerable annoyance may sometimes be avoided. It will be noticed that the hub of the wheel is counterbored at b ; the reason for doing so is to allow the full diameter of the axle to extend into the wheel, bringing the shoulder of the wheel fit inside of the hub, instead of against the hub, as explained in Art. 247. The object of this design is to prevent the breaking of the axle, which occasionally occurs when the shoulder of the wheel fit is pressed against the outside of the hub. The ribs m m, shown in Figs. 345 and 350, are for the purpose of stiffening the hollow rims. In some wheels the ribs are placed at the end of each spoke, as shown in Fig. 350 ; in other wheels they are placed at the end of each spoke and midway between them, as shown in Fig. 345. 250. Figs. 354 to 357 inclusive show different views of a driving wheel de- signed for an eight-wheeled passenger engine having cylinders 19 inches in diameter. In this wheel the spokes and rim are cast solid. One peculiarity of this wheel, not often found in others, is that the rim of the wheel center has a shoulder against which the tire is pressed. The object of this shoulder is to prevent the tire from slipping inwards when the flange is working against the rail. At first sight, it may appear that a shoulder of this kind is unnecessary, but when locomotives are fitted up with driver brakes, and these applied, the tire will in some instances become sufficiently hot to expand and thereby loosen it, and hence the importance of the shoulder will be apparent. We also notice that for these wheels the wheel fit is tapered ; its large diameter is the same as that of the journal, and consequently there are no shoulders, such as shown in Figs. 341 and 342. This is another method sometimes adopted for the prevention of breaking the axles near or at the hub of the wheel. The rim of this wheel is cored through in two places r r, and at the center r z of the counterbalance. In our opinion, the positions of the openings r r r 2 are better located than the two openings shown in Fig. 350 ; because in Fig. 354 the distances between the openings are nearly equal, and the openings r r through the rim are placed between such spokes where the strength of the hub is reinforced by ribs cast between the spokes, the result being that in this wheel the openings through the rim will not widen as easily nor as much as the openings in the wheel shown in Fig. 350, when the axle is forced into the hub of the wheel 251. Figs. 358 to 362 inclusive represent a driving wheel designed for an eight- wheeled passenger engine having cylinders 18 inches in diameter. This wheel has solid spokes. The rim is cast hollow, but differs from those previously shown, in the fact that in this wheel the cored part in the rim does not extend to the periphery ; it Mnlii:i;\ LOCOMOTIf'E CONSTRUCTION. 219 220 MODERN LOCOMOTIVE CONSTRUCTION. is closed, as shown in Fig. 362, and indicated by the dotted lines in Fig. 358. The only openings in the rim of this wheel are the core holes w w ; ribs in the rim, similar to those marked m m in Figs. 345 and 350, are not used. The rim from u to u is cast solid, but the extra metal thus obtained is not sufficient for counterbalancing, and therefore two or four separate pairs of counterbalance weights, as the case may Section of Spokr through A. "T Section of Spoke through Ji. r _ J Section of Hint through C. <r -ax --- 4-; 2* ---- H JL- - 53% betwten fire* Fig. 389 require, are bolted between the spokes. These weights, and the manner of bolting them to the wheel, are illustrated in Figs. 388 and 389. The hub of the wheel is cored out at a a, having small core openings v v extending to the axle. In this wheel the spokes, as they extend towards the hub, incline outwards; wheels of this kind are sometimes called dished wheels. The object of placing the spokes in this position is to make room for a comparatively wide axle box; but there is a limit to the inclination of the spokes, for if they are brought out too far, it will be necessary to spread the cylinders also, which is always an objectionable feature. 252. The wheels are usually forced on the axle with a hydraulic press. The pressure should be equal to about 9 tons per inch of diameter, so that an axle 6 inches in diameter will be forced into the wheel with a pressure of 6 x 9 = 54 tons ; or an axle 7 inches in diameter, with a pressure of 7 x 9 = 63 tons. To add further security, keys are driven into the wheel and axle. These keys are generally made J inch square for axles less than 6 inches in diameter ; 1 inch square MODES* LOCOMOTIVE CONSTRUCTION. 221 for axles varying from 6 to 7 inches in diameter ; and 14 inches square for axles 7 indies ami over in diameter. The illustrations represent driving wheels such as are used on some of our promi- nent railroads; they have been taken directly from working drawings kindly given to the writer by locomotive builders for the purpose of illustrating these pages. The designs of these wheels also indicate the study and care bestowed upon this subject by master-mechanics, so as to obtain a strong and safe wheel, thereby greatly promoting the safety of the passengers: -!.">:!. Figs. 363 and 364 represent the two views of a driving wheel designed for a consolidation engine having cylinders 20 inches in diameter. Fig. 365 represents a section through the rim, and Figs. 366, 367 represent sections of one of the arms. These are cast solid, the rim hollow, its form being similar to that of the rim shown in Fig. 358. The counterbalance weight is cast solid throughout, without any openings to prevent shrinkage stress. Figs. 368 and 369 represent two views of another driving wheel designed for a consolidation engine with cylinders 20 inches in diameter. The construction of this wheel is somewhat different from that shown in Fig. 363 ; it has hollow spokes and a hollow rim, the hollow part of the rim extending to the periphery of the wheel and strengthened by the ribs m m; the counterbalance has for the purpose of avoiding shrinkage stress openings r r cast into it, and extending to the rim. In Fig. 368 we see that the inner face of the wheel center projects beyond the inner face of the tire. This style of wheel is adopted for locomotives designed for roads having tracks of 5 feet gauge, which in the near future are to be reduced to a gauge of 4 feet 8 inches. Now, locomotives designed for a 5 feet gauge, and having the tires placed on the wheel centers, as shown in Fig. 368, can readily be changed to suit a gauge of 4 feet 8 inches, as all that need be done is to heat the tires and move them inwards on the wheel centers, and then turn off the outer face of the latter to suit the tires. COUNTERBALANCE. 254. In traveling in a railroad car it may sometimes be noticed that the motion of the train is not uniform, but is accompanied by jerks occurring at regular intervals. This kind of irregular motion is often due to the locomotive, which is imperfectly counterbalanced. Consequently, we may say in a general way that in a locomotive, all parts whose weights have a bad influence on the smooth forward and backward motion of the engine, and tend to produce jerks in its motion, must be counter- balanced; and therefore not only the weight of the crank and its pin, and other parts attached to the crank-pin which have a rotary motion, must be counterbalanced, but also those parts which are attached to the crank-pin and haves a reciprocating motion. Hence in locomotives the weights of the cranks, pins, connecting- and side-rods, piston-rods, crossheads, and pistons must be counterbalanced.* In order to explain as clearly as possible the method of counterbalancing these A difference of opinion exists in regard to the amount of weight to be counterbalanced, as will be seen farther on. 222 MODERN LOCOMOTIVE CONSTBVCT1OX. UODERX LOCOMOTirE CONSTRUCTION. 223 axle 224 MODERN LOCOMOTIVE CONSTRUCTION. parts of the engine, and reduce this subject to simple problems, we will first consider the principles upon which the method is based, and the application of these principles to the method used for finding the counterbalance for objects of simple outline. In the first place, then, we will determine the amount of counterbalance required for a crank such as is shown in Fig. 370. This crank is supposed to be of equal thickness throughout, and its form is perfectly sym- metrical that is to say, the diameter of the hole for the axle is equal to that of the hole for the crank- pin, the ends of the crank are exactly alike, and the depth c d or e /the same throughout. ria 370 Assume now that the crank stands in a hori- zontal position, as shown in our illustration, and that it is divided by vertical planes represented by the lines c d, ef, etc., into any number of parts ; then the weight of each part with a leverage corresponding to the distance between it and the center a of the axle will act with a certain amount of energy, tending to turn the axle around its center, bringing the center line a b of the crank in a vertical position below the axle. Now, in order to enable us to compare readily the amount of this energy with that of a force applied to some other point at a given distance from the center a, we assume that the weights of the different parts c d, ef, etc., of the crank are concentrated on the line a b at a single point i, so that the same amount of energy be developed as is developed by distributing the weight of the parts along the center line a b ; this point i will coincide with the center of gravity of the crank. Hence our first step will be to determine this center of gravity. The center of gravity of every solid or body is a point about which all the parts of the solid acted upon by the force of gravity balance each other, so that, if the solid be suspended from that point (center of gravity), the solid will be in equilibrium in any position it may be placed. Since the crank represented in Fig. 370 is symmetrical, its center of gravity i must lie in the center line a ft, and midway between the centers a and I. Hence in this case the center of gravity i is obtained without any calculation. After the center of gravity has been determined, we may assume that the distance between the center a of the axle and the center of gravity i represents the length of an arm of a lever whose fulcrum is at the center a. If the whole weight of the crank is applied to the extremity i of the lever arm a i, then the effect produced or the energy due to the weight applied to the end of the lever arm will be equal to the energy of the distributed weight of the crank. It is the influence of this energy, in counterbalancing the weight of the crank, that is to be destroyed by a force whose energy is equal and acting opposite to that due to the weight of the crank. By the assumption that the whole weight of the crank is concentrated at one point the center of gravity or applied to a point coinciding with the center of gravity, we obtain an easy way of comparing the energy developed by the weight of the crank and that developed by the counterbalance, and also an easy way for deter- mining the number of pounds of metal required in the latter. In determining the counterbalance we must also find its center of gravity, and, as MODKRX LOCOMOTIVE CONSTRUCTION. 225 in the case of the crank, assume its weight to be concentrated at its center of gravity. Those conditions will reduce the whole method of counterbalancing to a simple problem, in which the given conditions are such as represented in Fig. 371. In this figure the point a represents the center of the axle ; the line k b, passing through the center rt, represents a lever whose fulcrum is at a ; the line a b is the arm of the force C, its length is equal to the distance between the center of the axle and the center of gravity of the crank. The line a k is the arm of the force R, its length is equal to the distance be- ' " ' tween the center of the axle and the center of gravity of the counterbalance. The weight of the crank is represented by C which is attached to the point ft; the weight of the counterbalance is represented by .R, which is attached to the point k. Now, since in all levers of this kind which are in equilibrium the product ob- tained by multiplying the length of the arm a b by the weight 6', which is suspended from this arm, must be equal to the product obtained by multiplying the length of the arm a k by the weight It suspended from it, we can find the number of pounds of inetal required in the counterbalance by the following rule : RULE 42. Multiply the distance between the center of the axle and the center of gravity of the crank in inches by the weight of the crank in pounds, and divide this product by the distance between the center of the axle and the center of gravity of the counterbalance in inches ; the quotient will be the weight of the counterbalance in pounds. EXAMPLE 74. The length of the crank (Fig. 370) from the center a to the center b is 12 inches ; the weight of the crank is 300 pounds. It is required to find the weight of the counterbalance, which is placed so that the distance between its center of gravity and the center of the axle is 9 inches. Since the form of this crank is symmetrical, and since its length is 12 inches, the distance between its center of gravity and the center of axle is 6 inches ; hence we have, 6 x 300 ,. = 200 pounds; which is the weight necessary for counterbalancing the weight of the crank only. 255. In order to express concisely that which is to follow, it will be necessary to give a more general definition of the term " arm of the force," or simply " arm," and also a definition of the term " moment of a force " which we shall introduce. Fig. 371. Let k b represent a lever, a its fulcrum, It and C weights attached to the ends k and b of the lever. By the term " arm of the force " is meant the perpendicular distance from the ful- crum to the line of direction of a force applied to the arm. For instance: The weight C when applied to the end I of the lever will act in a vertical line b C, and therefore, according to our definition, the line a 6, which is perpendicular to the line I C, will If the arm of the force C. The line a k is the arm of the weight R, because <t /,- is the perpendicular distance from the fulcrum a to the line k R in which the weight It 226 MODERN LOCOMOTIVE CONSTRUCTION. acts. In fact, we may say that the arm of the force is the shortest line that can be drawn from the fulcrum to the line of direction of the force. By the term " line of direction of a force " is meant a line indicating the direction in which the force acts ; the length of this line is not limited by the distance between the arm and the weight attached to it. Thus, in Fig. 372, let the lever on one side of the fulcrum be bent as indicated by the line d a. In this case the line of direction in which the force, due to the weight R, acts is not limited by the end of the lever d and the weight R, but the line of direction is represented by the line d e extend- ing below the fulcnim, so that the line a k can be drawn from the fulcrum a per- pendicular to the line of direction d e. In this case the line a & is the ami of the weight R. Since the weight E acts with a leverage a k, we say that a k is IPs arm, and for a similar reason we say that a b is C's arm. MOMENT OF A FORCE. 256. The moment of a force with respect to a point is the product obtained by multiplying the force by the perpendicular distance from the point to the line of direction of the force. When the forces are applied to a lever, then the product of each force multiplied by its arm is the moment of that force. Thus : In the lever k b, Fig. 371, the force due to the weight R tends to turn the lever around the point or fulcrum a, and the same thing may be said of the force due to C, that is, it tends to turn the lever around the same fulcrum , but in an opposite direction. The weight E acts with a leverage a , hence the product of the weight R multiplied by its arm a k is the moment of the force due to the weight R. In like manner, the product obtained by multiplying the weight C by its arm a b is the moment of the force C. The moment of a force is used as a measure of its tendency to turn the lever around a point, or the fulcrum a. By establish- ing this measure we obtain an easy method for comparing the effect of the two forces applied to Fig 372 fc^] a ^ ever 5 ^ a ^ * s * sav > we can 1>ea( lily determine whether the forces applied to a lever will hold it in equilibrium or not ; and if these forces do not hold the lever in equilibrium, we are enabled to calculate quickly the amount by which one of the forces must be increased or decreased, and this is exactly what we have to do in counterbalancing some of the weights in a locomotive. When a lever is in equilibrium, the moments of the forces are equal to each other. To make the foregoing principles clear let us take the following example : EXAMPLE 75. Suppose that in Fig. 371 the length of the arm a k is two feet, and the weight R attached to it is 150 pounds, the length of the lever arm a b is four feet, and the weight C is 75 pounds. Will the lever k b under these conditions be in equi- librium ? The moment of the force due to R is equal to the product of the weight R into its arm a k; hence we have: 150 pounds x 2 feet = 300 foot pounds = moment of R. \ LOCOMOTIVE CONSTRUCTION. 227 The moment of the force C is equal to the pi-oduct of the weight C into its arm a //, hence \ve have: 75 pounds x 4 feet = 300 foot pounds = moment of C. Here, then, we see that the moments of the weights R and C are equal, and conse- quently the lever must be in equilibrium. Let us take another example. EXAMPLE 76. The length of the arm a k in Fig. 371 is two feet, the weight R attached to it is 300 pounds ; the length of the arm a b is four feet, and the weight (' attached to it is 75 pounds. Will the lever under these conditions be in equi- librium? If not, what change must be made in the weight R1 The moment of the weight R is equal to 300 pounds x 2 feet = 600 foot pounds. The moment of the weight C is equal to 75 pounds x 4 feet = 300 foot pounds. Here we see that the moment of R is 600, and the moment of C is 300, and since the moments are not equal, the lever cannot be in equilibrium. This also indicates, that because the moment of R is greater than the moment of C, the weight of R is too great, and consequently it will turn the lever around the point or fulcrum a and pull the end k downwards. In order to produce equilibrium, we would have to change one of the arms, or change one of the weights; but according to the conditions given in our example, we can make only one change, and that is in the weight R. Hence, our next step will be to determine by calculation the amount of reduction in the weight R. We have seen that in order to produce equilibrium the moments of the two forces must be equal. We know that the moment of the weight C is 300, and we also know that the length of Rs arm is 2 feet; now, since the product of 2 feet into the weight R, that is, the moment of 72, must be equal to 300 to produce equi- librium, we simply divide the moment of C by the length of R?s arm and obtain 300 - = 150 pounds for the weight of R. Here we see that R must be reduced to one- m half of its original weight. In calculating the moments we must always use the same unit of length for both lever arms, and also the same unit of weight for the forces applied to the lever. That is to say, when we multiply the arm a k in feet by the weight of R in pounds, we must also multiply the arm a b in feet (not inches) by the weight of C in pounds. If we multiply the arm a k in inches (which we are at perfect liberty to do) by the weight R in pounds, then we must also multiply the lever arm a b in inches (not feet) by the weight C in pounds. Or, if we adopt ounces as the unit of measurement for the weight R, we must also adopt ounces for the unit of measurement for the weight C. To make this plain, let us consider the conditions given in Example 76, namely, that the arm a k is equal to 2 feet, the arm a b equal to 4 feet, the weight R equal to 300 pounds, and the weight C equal to 75 pounds. Taking feet as the unit of measurement for the length of the arms, we have, for the moments of R and C: 300 x 2 = 600 foot pounds = moment of R ; and 75 x 4 = 300 foot pounds = moment of C. Here we see that the moment of R is equal to twice that of C. 228 MODERN LOCOMOTIVE CONSTRUCTION. Taking inches as the unit of measurement for the length of the arms, we have for the moments of E and C: 300 x 24 = 7200 inch pounds = moment of E ; and 75 x 48 = 3600 inch pounds = moment of C. Here, again, the moment of E is equal to twice that of C. Hence we see that, for the purpose of comparing the effects of the forces applied to the lever, it makes no differ- ence whether we adopt feet or inches for the unit of measurement, so long as we keep the same unit for both arms. If these principles are understood, considerable of the difficulty in determining the counterbalance for an engine will disappear. AMOUNT OF COUNTERBALANCE. 257. In Art. 254 it was seen that in determining the counterbalance for the crank, we simply assumed the line drawn from the center of gravity of the crank to the cen- ter of gravity of the counterbalance to represent a lever with the fulcrum at the center of the axle, and then calculated the weight attached to one end of the lever that would counterbalance the total weight of the crank attached to the opposite end of the lever. As we proceed, it will be seen that, for the sake of convenience in calculating the total amount of counterbalance required in a locomotive, it is desirable to adopt, in place of the whole weight of the crank applied to its center of gravity, a smaller weight applied to the center of the crank-pin, which will have the same effect as the whole weight of the crank applied to its center of gravity. This smaller weight is determined in the following manner : EXAMPLE 77. Fig. 373. Let a represent the center of the axle, and let the horizontal line k d drawn through a represent a lever with its fulcrum at a ; also let a d repre- sent the length of the crank that is, the distance between the center a of the axle and the center d of the crank- || pin; b the center of gravity of the crank; C the whole weight of the crank applied to b ; and E the weight of the counterbalance applied to the point k coinciding with the center of countenance - " gravity of the counterbalance. Let the total weight of the crank be 300 jf'iff, o / *> pounds, the length of the crank 12 inches, and the distance from the center of axle to the center of gravity k of the counterbalance 9 inches, and the distance from the center of axle to the center of gravity of the crank 6 inches; it is required to determine by calculation the weight W applied to the center d of the crank-pin ; the weight W is to have the same effect or tendency to turn the crank around the center a of the axle as that of the whole weight of the crank (300 pounds) applied to the center of gravity b. We have seen in Example 74 (Art. 254) that to counterbalance the weight of this MODERX LOCOMOTIVE COySTKUCTIOX. 229 crank under the given conditions, we require 200 pounds, and this countei'balance cannot be changed as long as the weight of the crank, its center of gravity, and the center of gravity of the counterbalance remain as they are given. But we have already seen that the moment of a force is a measure of its tendency to produce rotation. The moment of the counterbalance R in our example is equal to I'll!) x f) = 1800 inch pounds; and if the lever A: b is to remain in equilibrium, the moment of weight 6' must also be equal to 1,800 inch pounds, which we find to be the case in this example, for the distance from the center a of the axle to the center of gravity of the crank is G inches, and the weight of the crank is 300 pounds, hence the moment of C is 300 x = 1800 inch pounds. If we now replace the weight C of the crank applied to its center of gravity by another weight W applied to the center of the crank-pin d, and at the same time preserve an equilibrium, it will easily be perceived that the moment of W must be equal to the moment of R. Again, since the moment of C, as we have shown, is equal to the moment of R, we may say that the moment of W must be equal to the moment of C. Thei'efore, when to the center d of the crank-pin a weight W is to be attached, which shall have the same tendency to turn the crank around the center a of the axle, we have, for determining the amount of the weight IF, the following nile : KULE 43. Multiply the distance from the center of gravity of the crank to the center of the axle in inches by the total weight of the crank in pounds ; divide this product by the length of the crank in inches; the quotient will be the number of pounds in the weight W. Therefore, the required weight W in our example will be 6 inches x 300 pounds TTT; c~ ~ = 150 pounds 12 inches Generally in locomotives the center of gravity of the crank is not in the center of its length ; but Eule 43 will apply to all cases in which the center of gravity is in the center of the length or otherwise. How the center of gravity in bodies of different forms can be obtained will soon be explained. The advantage of determining the weight W applied to the center of crank-pin in place of the whole weight C of the crank applied to its center of gravity, is, that the counterbalance for the crank and other parts attached to the crank-pin, which must also be counterbalanced, can be found with less labor. POSITION OF THE CENTER OF GRAVITY OF THE COUNTERBALANCE. 258. So far we have assumed that the center of gravity of the crank and that of the counterbalance lie in one straight line passing through the center of axle. We have also stated that the length of the arm of the counterbalance is equal to the dis- tance between the center of the axle and the center of gravity of the counterbalance. It is now to be explained how the position of the center of gravity of the counterbal- ance can be determined. Let the full lines in Figs. 374 and 375 represent two views of a counterbalance; it is required to find the distance between its center of gravity and center of the 230 MODERN LOCOMOTIVE CONSTRUCTION. axle ; the arc / b tj is described from the center of the axle, and its radius is 11 inches. The middle point b of the arc fb g, the center of gravity of the weight, and the center of axle are to lie in one straight line. From the conditions given, we know that the distance from the point I to the center of axle is 11 inches ; it therefore remains to find only the distance between I and the center of gravity of the weight. Fig. 375 shows that the thickness of the weight is the same throughout ; we have, therefore, two methods for finding the position of its center of gravity : first, a geomet- rical method ; and second, a practical method. GEOMETEICAL METHOD. For the purpose of finding the distance between the center of gravity and the point b when the thickness of the weight is uniform, we have only to find the center of gravity of the surface or plane e a d g If, Fig. 374. Fig. 374. Join the points e and d by a straight line, and bisect this line by the perpendicular line a b, cutting the arc / g in the point I. The line a b will divide ill tnclies tu centre of axle Fig. 375 fig. 374 the plane e a d g b f into two equal parts, and is therefore a center line ; it also contains the center of gravity of the plane, because it passes through the centers of all lines drawn parallel to the line e d. Through the point b draw a line h i perpendic- ular to a b, cutting the line e /in the point 7i, and the line d g in the point i. For the sake of simplicity we will now consider the plane to be bounded at the ends by the straight lines e d and h i in place of the arcs e a d and / b f). Join the points d and h by a straight line d h, bisect this line that is, find the point j midway between the points d and 7t; join the points,/ and e, also the points,/ and ?, by the straight lines ej andj i. Divide the line e j into three equal parts, and thus obtain the point A-, which is the first point of division from the line d Ji. Also divide the line j i into three equal parts, thereby obtaining the point I, which is the first point of division from the line d Ji. Join the points k and,/ by a straight line k J cutting the line a b in the point C; this point C will be the center of gravity of the plane e d h i that is, the center of gravity of the plane bounded by the straight lines e d, h i, e h, and d i ; but it will not be the exact center of gravity of the plane bounded at the ends by the arcs e a d and fig', for all practical purposes we may consider the point C to be the center MODERN LOCOMOTIVE CONSTRUCTION. 231 of gravity of the plane bounded by the arcs, as in this case the error will not amount to more than i inch that is to say, the distance between the point a in the arc e a g and the center of gravity C found by the foregoing construction, will only be inch greater than the distance between a and the true center of gravity of the plane bounded by the arc end and/ b g. To prove that the point C is the correct center of gravity of the plane e d hi, it may be stated that the line d h divides the plane into two triangles, d e h and d h i; the point k is the center of gravity of the triangle d e h, and the point / is the center of gravity of the triangle d h i. We may now consider the two triangles to form a system of bodies ; under these conditions the point about which the two triangles will balance each other must lie in a line joining the centers of gravity k and I; but the two triangles make up the plane d e h /, and we have seen that the center of gravity of this plane must lie in the center line a &, therefore its center of gravity C must be the point in which the lines a b and k I intersect. To show that the method of finding the centers of gravity A; and I of the triangles is correct, we have the following demonstration, taken from " Theoretical Mechanics," by J. Weisbach. In a triangle d c h, Fig. 376, every line drawn from an angle to the center of the opposite side will contain the center of gravity of the triangle. Thus the line e m drawn from the angle e to the center in of the opposite side d h will contain the center of gravity, because the line e m bisects all lines such as o p, r s, which are drawn parallel to the side d h. The line d n drawn from the- angle d to the center n of the opposite side c h will also contain the center of gravity of the triangle, because the line d n will bisect every line drawn par- allel to the side c h, and therefore the point of inter- section k of the two lines e m and d n must be the center of gravity of the whole triangle. Join the points n and m by a straight line ; this line m n must be parallel to the side e d, because the line m n is drawn from the center of the side e h to the center of the side d Ji. Again, the length of the line n in must be equal to one-half of the length of the side d e, because the line n m is drawn from the center n of the side c h parallel to e d. Since n m is parallel to d e, it follows that the triangles ; n k and d e k are similar ; and because m n is equal to one-half of e h, the line m k is equal to one-half of the line e k, and consequently the line k m must be equal to one-third of the whole line e m. Hence the center of gravity k of the triangle <l < h is at a distance equal to J e m from the middle point m of the side d li, and at a distance equal to e m from the angle e. Fig. 376 ri;.\(TICAL METHOD. _>.">!). Before the pradiral method for determining the center of gravity is explained, let us first obtain an insight into an important property of gravity. Let the outline in Fig. .'!77 represent the shape of an iron plate of equal thickness through- 232 MODERN LOCOMOTIVE CONSTRUCTION. out, and let A, B, C, and I) represent holes drilled anywhere near the edges of this plate. Assume now that from a pin driven into a wall the plate is suspended by the hole A, the diameter of the pin being a little less than that of the hole, so that the plate can freely turn on the pin. We now find that after the plate has made a few oscillations, it will come to rest in only one position ; even if we withdraw it from this position, the plate, as soon as it is free to move, wih 1 again come to rest in the same place. Let us carefully mark this position ; to do so, we suspend a chalked line /* i, and plummet from the pin; then, when the plate is at rest, we carefully snap the string against the plate and thus obtain on the plate a chalked mark which represents a vertical line drawn through the center of the hole A. We now remove the plummet and suspend the plate by the hole B, then replacing the plummet we draw on the plate in the same manner as before another vertical chalked line through the center of the hole B. In a similar manner we suspend the plate, in succession, from the holes C and D, and from the center of these holes draw vertical chalked lines, thereby obtaining four chalked lines, which are represented in the figure by broken lines drawn through the centers of the holes A, B, C, and D. We now find this remarkable Fig. 877 condition, namely, all these lines will intersect in one and the same point G. If ad- ditional holes, E, F, and //, are drilled anywhere in the plate near its edge and the plate suspended from these holes in succession, and chalked lines drawn in a manner as described, we will find that these additional lines through the centers of the holes E, F, and H will also pass through the same point G. This point is the center of gravity of the plate. Hence we may say that a vertical line drawn through the point from which the plate is suspended will pass through or contain the center of gravity of the plate. The lines which pass through the center of gravity of a body are called " lines of gravity." In precisely the same manner we can find the position of the center of gravity LOCOMOTIVE COXSTRTCTIOX. 233 of the weight shown in Fig. 374, thus : Cut a templet to the form of the surface shown in Fig. 374. When the templet is to be cut to full size, it will be best to make it of wood; its thickness must be the same throughout; indeed, this condition is very important; the real thickness makes no difference; it may either be or J of an inch, or 1 inch, but it must be uniform. When the templet is to be cut to a scale, it may be made of stiff paper ; in this case care must be taken to keep it perfectly flat. On this templet draw the center line a b ; this line will contain the center of gravity. Anywhere in and near one of the corners of the templet, punch a small smooth hole, and from a pin suspend the templet by the hole, as shown in Fig. 378. In doing so care must be taken to allow the templet perfect freedom to turn on the pin. From the same pin suspend a plummet line, and when the templet is at rest mark off the point C in which the plummet line intersects the center line a b ; this point C will be the center of gravity of the surface shown in the figure, and will give the distance between the center of gravity of the weight and the point b, which is equal to 4 inches. Therefore the distance between the center of axle and the center of gravity of this counterbalance, which was to be found, is equal to 11 + 4 = 15 inches. Or, we may say, the arm of the counterbalance is 15J inches long. 260. In order to become familiar with the principles given in the previous articles, we will apply them to a simple case. EXAMPLE 78. Let a in Fig. 379 represent the center of the axle, b the center of the crank-pin; the distance between these two centers is 12 inches; ijkl represents the cast-iron crank, which is of uniform thickness. The weight of the crank is 250 pounds. In addition to this weight of the crank, another weight 111 of 100 pounds is applied to the center b of the crank-pin. One view of the couutei'balance is shown by the outline e d fh, and all the dimensions of the counterbalance except its thickness are given. The edge//* of the counterbalance is to be placed 11 inches from the center a of the axle; the center line op, and the center line a b of the crank, are to lie in one straight line o b. It is required to find the weight of this counterbalance, which will hold in equilibrium the sum of the weight of the crank and the additional weight of 100 pounds applied to the center b of the crank-pin. It is also required to 234 MODERN LOCOMOTIVE CONSTRUCTION. find the thickness of the counterbalance. Our first step will be to find the center of gravity of the crank and also that of the counterbalance. In order to avoid hereafter a misunderstanding, we deem the following remarks necessary. In these calculations, and in fact for all calculations employed for deter- mining the counterbalance in locomotive wheels, we only need to know the positions of the centers of gravity that is to say, we need only to know the distances of the centers of gravity of the crank and the counterbalance from the center of the axle. Hence, for the sake of brevity, we shall speak of the center of gravity as if it was located in the surface of the crank or counterbalance, whereas in reality it lies in the center of the thickness. Thus, in saying that G is the center of gravity of the crank, it must be understood that the point G simply indicates the distance of the center of gravity from the center of the axle, or the position it occupies between the center a and I. To find the center of gravity of the crank, cut out a templet to the shape of the crank, and on this templet draw the center line a b. Anywhere near the edge of the templet punch a small smooth hole w, and then suspend the templet by the hole n from a pin, as shown in Fig. 377, allowing it to have freedom to oscillate. From the same pin suspend a plummet line and mark off the point G in which the plummet line intersects the center line a I ; this point G will be the center of gravity of the crank. Suppose, now, that by this method we have found the distance between the center of gravity G and the center a of the axle to be 3 inches. To find the center of gravity of the counterbalance c dfh, we proceed in a manner as shown in Fig. 378, and explained in Art. 259. Also assume that by this method we have found the distance between the center of gravity C and the edge/ h to be 4 inches. Since the distance between the edge fh and the center a of the axle has been given, namely, 11 inches, it follows that the total distance between the center a and the center of gravity C must be equal to 11" + 4" = 15 inches. Our next step will be to find the weight, which, when applied to the center b of the crank-pin, will have the same effect in producing rotation of the crank around the center a as that of the weight of the crank applied to its center of gravity G. This weight is found by Eule 43, given in Art. 257. Hence we have, 250 pounds x 3j inches =7^ ; = 72.91 pounds. 12 inches This weight of 72.91 pounds applied to the center b will have the same tendency to produce rotation as the weight of the crank (250 pounds) applied to the center of gravity G, and therefore the 72.91 pounds applied at b will require the same counter- balance as 250 pounds applied at G. But to the center b of the crank-pin is to be applied an additional weight of 100 pounds, represented by m. Consequently, the total weight applied to the crank-pin, and which must be counterbalanced, is 172.91 pounds. We may now reduce our problem to a very simple one. Thus : Fig. 380. Let the line c b represent a straight lever, and a its fulcrum ; the distance between the fulcrum a and the end b of the lever arm is equal to the distance between the center U)i k-- 19 i\ MODERN LOCOMOTIVE CONSTRUCTION. 235 of axle aiid the center of crauk-pin, namely, 12 inches; and the distance between the fulcrum a and the end c of the other lever arm is equal to the distance between the (liter of the axle and the center of gravity of the counterbalance, namely, 15 inches. Now we know that the weight applied to the end l> is equal to 172.91 pounds, consequently all we have to do is to find the amount of weight, which, when applied to the end c, will hold the lever in equilibrium. To find this weight, or, we may say, to find the weight of the counterbalance for any given weight on the crank-pin, we have the following rule : RVLE 44. Multiply the distance in inches between the center of the axle and the center of the crank-pin by the total weight in pounds applied to the crauk-pin, and divide this product by the distance in inches between the center of the axle and the center of gravity of the counterbalance; the quotient will be the weight in pounds of the counterbalance. According to this rule, we have, 172.91 pounds x 12 inches - = 133.86 pounds, 15 pounds which is the weight of the counterbalance. In order to find the thickness of this weight or counterbalance, we must first find the number of cubic inches contained in it. One cubic inch of cast-irou is generally reckoned to weigh .26 of a pound ; hence the following rule : RULE 45. Divide the number of pounds in the counterbalance by .26; the quotient will be the number of cubic inches in the counterbalance. The number of pounds in our counterbalance is 133.86 ; consequently, according to Rule 45, 133.86 .26 = 514.84 cubic inches in the counterbalance. To determine the thickness of the counterbalance, we have the following rule : RULE 46. Divide the number of cubic inches contained in the counterbalance by the area in square inches of its face ; the quotient will be the thickness of the counter- balance in inches. The area of the face e d f h (Fig. 379) is found by multiplying one-half the sum of the parallel sides ed and / h by its length o p; the product will be the number of square inches in the, surface r </ /'//. Thus: ft -^- 3" x 8" = 40 inches. -j Now, according to Rule 46, the thickness of the counterbalance will be, 514.84 cubic inches , - = 12.8 / inches, say 121 inches. 40 square inches 261. Generally in locomotives there is not sufficient room for a counterbalance 12 indies in thickness, consequently we must employ two weights, each similar in form 236 MODERN LOCOMOTIVE CONSTRUCTION. to that shown in Fig. 379, so that the thickness can be reduced and still have sufficient weight for counterbalancing. EXAMPLE 79. Let i j k I, Fig. 381, represent the same cast-iron crank of 250 pounds, and m the same additional weight of 100 pounds applied to the center of the crank-pin, as given in Example 78. The sum of the weights of this crank and weight m are now to be counterbalanced by two weights whose dimensions, except their thicknesses, are given, and these dimensions of each weight are the same as those of Fig. 381 the weight given in Example 78. The space between the two weights is equal to the thickness of the spoke of the wheel ; the weight of the spoke, as in the previous example, is, for the sake of simplicity, left out of consideration. The edge fh of the upper weight is to be placed 11 inches from the center a of the axle, and the same distance is to be maintained between the edge f. 2 Ii 2 of the lower weight and the center a. In fact, the only difference between this example and the former one is that two weights for counterbalancing, instead of one, are to be used. It is required to find the number of pounds in these weights and their thickness. Since the size and weight of the crank, and also the additional weight m, are the same as before, it follows that the total weight as considered to be applied to the crank- pin will be 172.91 pounds, and this weight must be counterbalanced. Again, since the size of each counterbalance weight, except the thickness, is equal to the size of the weight shown in Fig. 379, it follows that the center of gravity C of the upper weight must be in the same relative position as before that is, the distance between the center of gravity C and the edge / h must be equal to 4i inches. The same remarks apply to the center of gravity C 2 of the lower weight. Consequently the distance between the centers (7 and a will be equal to 15 inches, and the distance between the center C 2 and will also be equal to 13 inches, both distances remaining the same as in the previous example. We may now consider the weight e d fh, and the weight e. 2 (I,f 2 1> 2 to be segments of one counterbalance. Now, considering these two weights to form one counterbalance e d 2 f 2 h, it must be apparent that neither the center C nor the center C 2 can be the center of gravity of the whole counterbalance e d. 2 f, /< ; we must therefore find a new center of gravity JV, or we may say a common center of gravity of the two segments e dfh and e., d 2 f 2 h 2 . To find this new center of gravity, we simply join the centers UODERX LOCOMOTIVE CONSTRUCTION. 037 C and C-2 by a straight line; the poiut N in which this line cuts the center line r b will be the center of gravity required. Now assume that, by this construction, we find the distance between the center of gravity N and the center a of the axle to be equal to 15 inches; we have then all the data necessary for determining the weight and thickness of the counterbalance. In fact, we may now reduce our problem to that of the simple straight lever, as shown in Fig. 380, in which the line c b represents the lever, a the fulcrum, a b a lever arm 12 inches long, and c a the other lever arm 15 inches long. To the end b is applied a weight W of 172.91 pounds. It is now required to find the weight li, which, when applied to the end c, will hold the lever in equilibrium. It will be noticed that the only difference between this problem and the previous one represented by this figure consists in the length of the lever arm c a, which in the previous problem was 15 inches long instead of 15 inches, as we must now consider it to be. Remembering that the new center of gravity N is the common center of gravity of the two segments, and is the only center of gravity that can now enter in our calcula- tion, we can find the sum of the weights of the segments by Eule 44. Hence we have 172.91 pounds x 12 inches rrr- - = 138.32 pounds, 15 pounds which is the sum of the weights of the two segments. Consequently the weight of one segment will be 138.32 ^ = 69.16 pounds. a It will be noticed that in this example the sum of the weights of the two segments is somewhat greater than the weight of the counterbalance used in Fig. 379, and yet in both examples the weights applied to the crank-pin, which were to be counter- balanced, are equal. This is as it should be, because in Fig. 381 the distance between the center of gravity N and the center a of the axle is less than that between C and a in Fig. 379. We have found that the weight of one segment of the counterbalance in Fig. 381 is equal to 69.16 pounds. In order to find the thickness of one of these segments, we must first find by Rule 45 the number of cubic inches contained in each segment. Hence we have, nr. = 266 cubic inches. Now, since we know the area of the face c d fh of one segment is equal to 40 square inches, the thickness of the segment will be, according to Rule 46, equal to 266 cubic inches = 6.65 inches. 40 square inches area 262. In Art. 261 we explained the manner of finding the common center of gravity of two segments of a counterbalance. When more than two segments are to be used a frequent occurrence the common center of gravity may be found by the following methods : 238 MODERN LOCOMOTIVE CONSTRUCTION. EXAMPLE 79a. Let A, B, D in Fig. 382 represent three segments of a counter- balance ; all these segments are equal in form and weight ; it is required to find the common center of gravity of these segments. RULE 47. Draw the three segments in their correct position that is, leaving the correct spaces for the spokes between them and draw the center lines e f, c 2 /. e 3 f 3 ; these center lines will, when produced, pass through the center of axle. Find the center of gravity of one of the segments, say of the segment B, by the method shown in Fig. 374, or by the method shown in Fig. 378, and thus obtain the center of gravity C 2 . From the center a of the axle draw an arc passing through the center C 2 , cutting the line e/in the point C, and the line e 3 f 3 in the point C 3 . Then C will be the center of gravity of the segment A ; and C 3 the center of gravity of the segment D. The centers C, C 2 , C 3 must lie in an arc described from the center of the axle, because the segments are all placed at equal distances from the center of axle, and are alike in form and weight. Through the points C and C 3 draw a straight line cutting the center line e 2 f 2 in the point i. Divide the distance between the center of gravity C 2 and the point Fig. 382 Fig. 383 Fig. 384 i into three equal parts ; the point of division G, which is nearest to the point i, will be the common center of gravity of the three segments. Here we see that the distance between G and i is equal to one-third of C 2 i. EXAMPLE 79b. Let A, J5, D, E in Fig. 383 represent four segments of a counter- balance ; all these segments are equal in form and weight ; it is required to find the common center of gravity of these segments. RULE 48. Draw the segments in their correct position, leaving the exact amount of space for the spokes between them. Two of these segments must lie above the line b , and two of the segments below it. The line I a must pass through the center of the space for the wheel spoke, and when produced pass through the center a of the axle and also through the center of the crank-pin. Draw the center lines ef,e 2 f 2 , e 3 f 3 , and e 4 / 4 . Find the center of gravity of one of the weights, say C of the segment A, according to the method shown in Fig. 374 or Fig. 378. From the center a of the axle describe an arc passing through the center of gravity C and cutting the line e 2 f 2 in MODKKX LOCOXOTirE COXSTRCCTIOX. 239 flic point ('.,, c-1 ,/3 in the point (7 3 , and c 4 f t in the point 6 4 . The point C 2 will bo the center of gravity of the segment B, C 3 the center of gravity of Z), and C 4 that of the segment E. Through the centers C and 6' 4 draw a straight line, cutting the line a b in the point /; ulso through the centers C 2 and G 3 draw a straight line, cutting b in the point It ; the point G midway between i and h will be the common center of gravity of the four segments. EXAMPLE 79r. Let A, B, Z>, E, F in Fig. 384 represent five segments of a counterbalance, all of them equal in form and weight ; it is required to find the common center of gravity of these segments. EULE 49. Through the center a of the axle draw the horizontal line a b ; on this line draw the segment D, making its center line e 3 fj coincide with a I. Draw the segments A and B above, and the segments E and F below, the segment D all in the correct position, with the correct spaces for the spokes between them. Find the center of gravity C 3 of the segment D, according to the method shown in Fig. 374 or Fig. 378. From the center a of the axle describe an arc passing through C 3 and cutting the center lines e f, <: 2 ./o, P 4 ,/ 4 , >' :> f :> of the segments A, B, E, F in the points C, C 2 , C 4 , C 5 ; these points will be the centers of gravity of their respective segments. Join the points Cand C' 5 by a straight line, cutting a b in the point i. Also join the points C 2 C 4 by a straight line, cutting a I in the point h. On the line a b lay off a point / midway between i and /<; and then divide the distance between I and G 3 into five equal parts. The point of division marked G nearest to the point / will be the common center of gravity of the five segments. The common center of gravity G of the five segments may also be found approximately, but often near enough for practical pur- poses, in the following manner : Cut a templet conforming with the outline I m fa n o of all the five segments shown in Fig. 384. This templet is represented on a smaller scale in Fig. 385. Any- where in this templet punch a small smooth hole b and suspend it by this hole from a pin, allowing it freedom to oscillate. From this pin suspend a plummet-line; the point G in which the plummet-line crosses the center line i b, previously drawn on the templet, is the center of gravity of the five segments. 263. A knowledge of the principles upon which the foregoing methods are based may not only prevent mistakes in the applications of the methods, but will also enable us to find the common center of gravity of a number of segments under varied conditions. In Fig. 386 we may consider the horizontal line G to d to represent a lever, whose fulcrum is at a that is, the center of the axle. This lever is held in equilibrium by the weight TFapplied at d, and the counterweights A and B applied at the end of the ot her lever arm. The segments A and I> are equal in form and weight, and are placed at equal distances from the center a of the axle, consequently their centers of gravity, C and (_'.# must also be at equal distances from tl enter . Again, since the distance Itetween the center of gravity (7 and tin- line // <\ is equal to that between the center G' 2 and the line b (/, it follows that the straight line C C., joining tin- centers of gravity 240 MODERN LOCOMOTIVE CONSTRUCTION. of the two segments must be perpendicular to b d. From statements made in previous articles, we may assume that the whole weight of the segment A is concentrated at the point C, and if this point C is left free to move, the force of gravity will cause it to move in the straight line C C 2 . Also the whole weight of the segment B may be considered to be concentrated at its center of gravity C' 2 , and if this point is left free w fig. 387 Fiff. 386 to move, the force of gravity will cause it to move in the same line C (7 2 prolonged. Therefore we may say that the line C C 2 is the line of direction in which the forces duo to the weights of the two segments act; and according to the remarks in Art. '235, the line G a, which is the perpendicular distance from the fulcrum a to the line of direction C C 2 , is the length of the arm, and we may consider the segments A and B to be directly applied to the point G ; or, in other words, we may assume that the sum of the weights of the two segments is concentrated at the point G, producing precisely the same effect in holding the lever in equilibrium as the combined effect of the weight of A acting at C, and the weight of B acting at C 2 . 264. But we may consider this problem in another light. Treating the two segments A and B as two distinct bodies, similar to those shown in Fig. 387, each one equal to any given weight that is to say, they may be, or may not be, equal in weight, placed in any given position, either one above the other, or side by side, or otherwise, the common center of gravity of these bodies or weights can be found in the following manner : Fig. 387. Let E represent one body weighing 10 pounds, and W another body weighing 5 pounds ; it is required to find the common center of gravity of these two bodies. RULE 50. First find the center of gravity c of the weight E, and also the center of gravity d of the weight W; join the points c and c? by a straight line ; this line will contain the common center of gravity G of the two weights E and W. Now, in order to find the exact location of the point G on the line c d, we have the following proportion : The sum of the weights E and W : the line c d : : weight of E : G d; or, The sum of the weights E and W : the line c d : : weight of W : G c. Now, supposing we find that by measurement the line c d is 12 inches long, then we have, (10 + 5) : 12 : : 10 : G d. Working out this proportion, we have, 12 x 10 MDI:I;\ i.ocoMorii /: c<>\srnrrTioy. 241 which shows that the common center of gravity G is located at 8 inches from d. Again, (10 + 5) : 12 : : 5 : G c. Working out this proportion, we have, 12 x 5 15 = 4 = G c, which indicates that the common center of gravity G is located at 4 inches from c. Now notice the product of the weight E multiplied by its arm G c is equal to the product of the weight W multiplied by its arm G d. This is as it should be, otherwise the solution is not correct, because G is the point about which the weights M and W must balance each other, and consequently the moment of the force R must be equal to the moment of the force W. (See Art. 256.) In Fig. 386 the weights of the two segments A and B are equal, and consequently, according to the foregoing rule, the common center of gravity G must lie midway between C and Co in a straight line joining these two points. The usefulness of Rule 50 will become apparent as we proceed. 265. Let us now examine the method for finding the common center of gravity of three segments as shown in Fig. 382. In the first place, let us assume that the center segment B has been removed ; in this way our problem becomes similar to that shown in Fig. 386, and we find that the point i (Fig. 382) in which the vertical line C C 3 cuts the horizontal line a e 2 is the common center of gravity of the two segments A and D. We now may assume that simply a weight equal to the sum of the weights of the segments A and U is applied at the point i, and throw the idea of segments A and D out of mind. Replacing the segment B in its proper position, and remembering that in determining the effect of this weight we assume the whole of the weight of the segment is concentrated at its r-iitcr of gravity C 2 , we have then two weights applied to the line a c 2 , namely, one at ( '., and the other at i ; the weight at i is twice as great as that applied at C 2 . Now to find the effect of these two weights we must find their common center of gravity G by Rule 50. For the sake of simplicity we will say the weight of the segment B is equal to 1 ; and consequently the weight applied at i will be equal to 2 ; hence we have, The sum of the weights at i and C 2 - 3 : line C. 2 i : : weight at C 2 : G i. Working out this proportion, and assuming that by measurement the line C 2 i is equal to Ij inches, we have, H x 1 o = inch = G i ; that is, the common center of gravity G is located inch from the point i towards C 2 . Now 4 inch is equal to i of li inches that is to say, G i = of C 2 i, which agrees with the previous construction. 266. Now let us take Fig. 383. Here we have four segments which make up the counterbalance. The point /' in which tin- line C C 4 cuts the line a I is the common center of gravity of the two segments .4 and E; and the point // in which the line ('., ('3 cuts the line a b is the common center of gravity of the two segments />' and I). 242 MODERN LOCOMOTIVE CONSTRUCTION. We may now assume that we have simply a weight applied at h, and another one at / ; and since the weights of the segments are equal, the weight applied at h is equal to that applied at i. In order to determine the effect of these two weights at h and i, we must find their common center of gravity G ; and since these weights are equal, we find, by Rule 50, that the common center of gravity G is located midway between /* and i, which agrees with the construction. 267. Lastly, Fig. 384. Here we find the counterbalance composed of five segments. The point i in which the line C C 5 cuts the line a b is the common center of gravity of the two segments A and F. The point h in which the line C 2 C\ cuts the line a b is the common center of gravity of the two segments B and E. According to the construction in Fig. 383, the point / in Fig. 384, midway between h and i, is the common center of gravity of the weights applied at li and i that is, of the four segments A, -B, E, and F. We may now assume that there are two weights applied to the line a I), one at / and another at C 3 . The weight at / is four times as heavy as that at C 3 . We may now determine the location of the common center of gravity G of the two weights, namely, the weight at (7 3 , and that applied at I by Eule 50 ; hence we have, The sum of the weights at I and C 3 = 5 : line C 3 I : : weight at C 3 : G I. Working out this proportion, and assuming that by measurement we find the line C 3 I to be equal to 3f inches, we have, 3f x 1 = inch = Gl\ But f that is, the common center of gravity is located at 3 inch from / towards C 3 . inch is i of 3J, which agrees with the construction. In all counterbalances which are composed of segments, we always consider the sum of the weights of the segments to be concentrated at their common center of gravity, and the distance from this point to the center of the axle that is, from G to a to be the lever arm. 268. Figs. 388 and 389 represent the form of one of the cast-iron segments of a counterbalance designed to be bolted between the spokes. As will be seen, this segment is made in two pieces, A and B. The piece A is placed in the outer face of the driving wheel, and B in the inner face of the wheel. They are held together and clamped to the wheel by the three bolts c c c 2 . In large wheels these bolts are of an inch diameter ; in small wheels, $ inch diameter. Since the space through which the counterbalance has to move is nearly Fig. 388 Fig. 3S9 always limited, the bolt heads are generally made conical and countersunk into the outer piece A ; in the inner piece B pockets / are cast to receive the nuts. The strips (j g are simply chipping strips, so that the weights can be snugly fitted between the spokes and rim. MODERX LOCOMOTII'K COSSTBUCTIOX. 243 The thickness of the outer piece A depends upon the available space through which in connection with the axle it can revolve. In some cases, the thickness of this piece depends upon the amount of weight required. The inner piece B is usually kept even with the spokes. The length d e also depends upon the amount of weight required, and varies from about one-half to three-quarters of the distance between the rim and hub of the wheel. These segments should never fill the whole space from rim to hub, because, if these spaces are closed by the segments, it will, when the wheels are in certain position, be very difficult to oil the axle journals. In calculating the weight of the counterbalance it is always best to establish first the length d e of the segment, and then find its thickness. EXAMPLE 80. It is required to find the dimensions of the segments of a coun- terbalance for an eight-wheeled locomotive that is, an engine having four driving wheels and a four-wheeled truck, such as is shown in Fig. 1. Cylinders, 18 inches in diameter; stroke", 24 inches; weight of crosshead, 154 pounds; piston and rod, complete, 306 pounds; main-rod, 280 pounds; side-rod, 240 pounds; crank-pin, 60 pounds. The form of wheel is shown in Fig. 390. Not only the revolving parts, but also the reciprocating parts of a locomotive will have a disturbing influence on the smooth running of the engine. To obtain a steady motion, the weight of all the parts which produce a disturbing influence must be counterbalanced. Engineers agree that the sum of the weights of all the revolving parts must be counterbalanced ; but as to the proportion of the weight of the reciprocating parts which ought to be counterbalanced, they are not unanimous. A few believe that only two-thirds of the weight of the reciprocating parts should bo counterbalanced. Our practice has been to counterbalance the sum of the weights of all the reciprocating parts, and we believe it is safe to say that this is the practice of the majority of engineers, and will give the best results; we will follow this practice in the example under consideration. In determining the dimensions of the counterbalance, we need to confine our attention to only one side of the engine, and consequently in our calculation we have to deal with only two driving wheels through which the counterbalance must be distributed. Each wheel should have enough weight to counterbalance one-half of the weight of the reciprocating parts, in addition to the total weight of the parts which revolve with the wheel. Hence our first step will be to separate the weights of the revolving and the reciprocating parts. The parts, and their weights, which revolve with the main driving wheel, are : Crank-pin 60 Ibs. Weight of crank referred to pin 180 " One-half side-rod 120 " One-half mam-rod 140 " Total weight of the revolving p.-n-ts .100 Ibs. The parts, and their weights, which revolve with the rear driving wheel, are: Crank-pin 60 Ibs. Weight of crank jvfenvd to pin 180 " One-half of side-rod 120 " Total weight of revolving parts 360 Ibs. 244 MODERN LOCOMOTIVE CONSTRUCTION. By the term weight of the crank referred to the crank-pin is meant that weight which, when applied to the crank-pin, will have the same effect in tending to turn the axle as the whole of the weight of the crank applied to the center of gravity of the crank, as explained in Art. 257. To find the weight of the crank referred to the crank- pin, we must first find the center of gravity of the crank by the method shown in Fig. 377, and then compute the weight by Eule 43. Of course, in this case, the thickness of the crank is supposed to be uniform. When the thickness is not uniform, another method is often adopted, which will be explained in Art. 270. Eeciprocating parts, and their weights, are : Crosshead, pin, etc 154 Ibs. Piston and rod 306 " One-half of main-rod 140 '' Total weight of reciprocating parts 600 Ibs. One-half of this weight must be counterbalanced in the main wheel, the other half in the rear wheel. Consequently, the total weight to be counterbalanced in the main driving wheel will be 500 + 300 = 800 pounds; and the weight to be counterbalanced in the rear driving wheel will be 360 -I- 300 = 660 pounds. We will first determine the dimensions of the segments composing the counter- balance in the main driving wheel. In this wheel we have to counterbalance 800 pounds applied to the crank-pin, and since the distance between the center of crank- pin and center of axle is 12 inches, the moment of the force produced by the 800 P UndsiS 800X12 = 9600. Our next step will be to establish the number of segments in the counterbalance, and also the length d e of each. No regular rules for determining the number of segments, and their lengths, can be given. An experienced engineer will readily see that four segments, A, B, Z), and E (Pig. 390), will be necessary. A smaller number of segments would make their thickness too great for the available space through which they have to move. Hence we will decide that four segments are to be used, and that the length d e of each one is to be 12 inches. We now find the center of gravity C of one of the segments in the manner shown in Fig. 374 or 378, and then find the common center of gravity G of the four segments by the method shown in Fig. 383 and explained in Art. 266. Measuring the distance between the common center of gravity G and the center a of the axle, Fig. 390, we find it to be 18f inches. Now, since the moment of force due to the weight of the four segments, that is, the product obtained by multiplying the total weight of the four segments by the 18f inches, must be equal to the moment of the force due to the weight applied to the crank-pin, namely 9,600 (previously determined), we can find the total weight of the four segments by Rule 44. Hence we have 800 x 12 9600 ~Ia75~ = 18.75 MODEBX LOCOMOTIVE COXSTRUCTIOy. 245 Since the weight of a cubic inch of cast-iron is .26 of a pound, the total number of cubic inches in the four segments will be, according to Eule 45, 512 -^ = 1969 cubic inches. .*io Assuming that in Fig. 390 the area of fg h i of one segment is 80 square inches, then the area of the four segments will be 80 x 4 = 320 square inches. And lastly the thickness of the counterbalance, or, which amounts to the same tiling, the thickness of each segment, will be, according to Rule 46, 1969 320 = 6.15+ inches. The dimensions of the segments for the rear driving wheel are found in a manner fig. 39O precisely similar to the foregoing that is, we first establish the length d e of the segments, and then find the thickness. We will make the calculations without explan- atory remarks. 240 MODERN LOCOMOTIVE CONSTRUCTION. Let us decide that the length d e of each one of the four segments in the rear driving wheel is to be 12 inches that is, equal to the length of segments in the main driving wheel. Under these conditions the common center of gravity G will be 18 inches from the center a of the axle, the same as in the main driving wheel. Now, remembering that the total weight applied to the crank-pin in this wheel, and which must be counterbalanced, is 660 pounds, we have, 660 x 12 1875 = 422.4 pounds, which is the total number of pounds in the four segments. Again, 422.4 .26 in the four segments, and lastly, = 1624 cubic inches 1624 - u inches, which is the thickness of each segment in the rear driving wheel. 269. It must be remarked here, that when the center of gravity C of one of the segments is to be found by the method shown in Fig. 378, the templet must be cut somewhat smaller than the face / g h i of the segment (Fig. 390), to allow for the amount of metal cut out of the segment for the spokes and rim. The reduction in the size of templet should be made in the length d e, bringing the arc/i closer to the arc g /; the reduction should be made at the end/i, none at g h, because the end g h is not to fit any part of the wheel, and consequently there is no metal cut out at this end. A small reduction should also be made in the width, bringing the two sides fg and h i closer together. The amount of reduction is generally governed by good judgment rather than by calculation, as the latter method is tedious and involves considerable labor. Any slight inaccuracy which may result can easily be corrected by finding the center of gravity of the pattern of the segment when made, which will enable us to correct any small error in the weight of the counterbalance by readjusting the common center of gravity G of all the segments, and make such slight changes in the pattern as may be deemed necessary. In many cases the required reduction of the templet will be so small that for practical purposes we may cut the templet to conform to the surface fg h i without making any reduction. It must also be noticed that the weight of the counterbalance, found in the manner as we have done, will be slightly very slightly too heavy, for the following reason : If the wheel center is made without the crank-pin hub, and if the workmanship is absolutely perfect, the wheel center itself will be perfectly balanced. In putting in the crank-pin hub, a portion F of the spokes must be cut out, and for this amount of metal thus cut out no allowance has been made, and consequently the counterbalance is not only sufficient for the weight of the crank, but also for the amount F cut out of the spokes, and therefore the counterbalance is slightly too heavy, but by an amount barely appreciable. MODERX LOCOMOTIVE COXSTKUCTrOX. 247 Fly. 391 270. Again, engineers and draftsmen often find it difficult to determine the exact location of the center of gravity of the crank, and therefore, instead of finding the weight of the crank referred to the crank-pin, content themselves by finding the weight of the crank-pin hub that is, the weight of the metal around the crank-pin as indicated by the shaded portion in Fig. 391 and then adding this weight to the revolving paiis to be counterbalanced, in place of the weight of the crank referred to the crank-pin ; by this method the neces- sity of finding the center of gravity of the crank is avoided. This method of adding the weight of the crank-pin hub to the revolving parts, _" ~ which must be counterbalanced, saves con- J siderable labor in all cases, and is usually adopted when the crank is not of uniform thickness. 271. Frequently, in fact in the majority of locomotives, the counterbalance and the wheel center are cast in one piece, as shown in Fig. 392. To determine the dimensions of a counterbalance of this kind, we should follow the rales given in Art. 268. That is to say, we should consider the solid coun- terbalance to be made up of a number of segments bolted between the spokes, as shown in Fig. 390, and then determine the thickness by a method precisely similar to that given in Art. 268. The correctness of the result of the calculation depends upon the correct position of the common center of gravity G (Fig. 390) of the segments, and this center, of course, depends upon the correct position of the center of gravity C of each segment ; therefore we conclude that when the centers of gravity C\ C 2 , etc., of the segments are placed in incorrect positions, the results of our calculations will be erroneous. If in these segments metal had not to be cut out of the sides i h and/// to fit the spokes, and also out of the end / i to fit the rim, we could find very accurately and easily the centers of gravity C l C 2 of these segments of unifonn thickness by the method shown in Fig. 378. But it is not such an easy matter to find the center of gravity of segments of irregular shapes, as shown in Fig. 390, or Fig. 389; in fact, to find correctly the center of gravity of one of these segments involves a great amount of labor, unless we have the pattern of which the center of gravity may be found by balancing it on a knife edge. Now, when a solid counterbalance, as shown in Fig. 392, is considered to be made up of segments, we cannot lose sight of the fact that the sides of the segments and their outer ends must be formed to fit the spokes, and consequently we have to do with segments of irregular shape. To reduce the labor of finding the common center of gravity of these segments, or, in other words, to reduce the labor of finding the center of gravity G of the counterbalance shown in Fig. 392, we may generally adopt the following method; the results obtained by this method, although not absolutely correct, will be sufficiently accurate for practical purposes: 248 MODERN LOCOMOTIVE CONSTRUCTION. Instead of considering the counterbalance (Fig. 392) to be made up of segments, as we should do, we treat it as it appears to be, namely, as one solid weight. Now, assume that the dimensions of this weight are such as will give a sufficient amount of metal, and not more, to counterbalance all the weights applied to the center of crank- pin ; then, by inserting, so to speak, this counterbalance into the wheel center, we must cut portions out of several spokes, and also cut a part out of the rim ; by so doing we leave unbalanced portions of other spokes and a part of the rim on the crank-pin side, all of which are precisely similar in amount and form to those cut out. It must be evident that by leaving portions of the wheel itself unbalanced we create new- disturbing forces, which will be just as injurious as a similar amount of unbalanced weight applied to the crank-pin. Therefore the thickness of our present counter- balance must be increased, so that not only the weights applied to the crank -pin are counterbalanced, but also have sufficient weight to counterbalance those portions of the wheel opposite those which had to be cut out to make room for the counter- balance. In the following example it will be seen how a close approximation to the exact thickness can be determined. EXAMPLE 81. The distance from the center of axle to the center of crank-pin is 12 inches ; the total weight applied to the crank, which must be counterbalanced, is L Fig. 393 Section through r.s Fig. 392 500 pounds ; the depth of the counterbalance from h to g is to be 8 inches, and is to terminate in the centers a b,fe of the spokes A and B (Fig. 392). It is required to find the thickness of the counterbalance ; this thickness is indicated by t, in Fig. 393. This figure represents a cross-section of the counterbalance through the line marked r s, in Fig. 392. In the first place, make a drawing of the wheel, as shown in Fig. 392, then cut a templet conforming to the outline a I hfeg of the counterbalance, and find its center of gravity G in the manner shown in Fig. 385. Mark off this center of gravity G on the drawing, and measure its distance from the center i of the axle. Assume that we find the distance between G and the center i to be 16 inches, we will then have all the data necessary for detei'mining the thickness by calculation. The moment of the force due to the weight applied to the crank-pin is equal to 500 x 12 = 6000. MODERN LOCOMOTIVE CONSTRUCTION. 249 The moment of the force due to the weight of the counterbalance must also be equal to 6,000 ; hence, by dividing 6,000 by the distance of the center of gravity G from the center /, we have, 6000 Tfr = 375 pounds, which is the weight necessary to counterbalance the weight applied to the crank-pin. But this counterbalance cuts portions out of five spokes and also a portion out of the rim. Suppose now that by calculation we find the total amount thus cut out of the wheel center to be equal to 80 pounds. Adding this weight to 375 pounds previously found, we have, 375 + 80 = 455 pounds for the total weight of the counterbalance. We now find the thickness of the counterbalance in a manner precisely similar to that given in Art. 268, thus : Dividing the total weight of 455 pounds by the weight of a cubic inch of cast-iron, we have, 455 ~n~ = 1750 cubic inches required in the counterbalance. And lastly, dividing the number of cubic inches by the area of the face a I It/eg of the counterbalance, we have, 1750 ~- = 6.83 inches, which is the thickness of the counterbalance. 272. The simplest way of finding the area of the surface a b life g of the counter- balance will be to describe an arc m n o midway between the arcs age and b hf(not drawn through the center of gravity <?), then find by measm-ement the length of the arc >n n o, and multiply this length by the depth a b ; the product will be the number of square inches in the face of the counterbalance. 273. Now it must not be understood that we claim to obtain, by the foregoing 1 1 n -t hod, an absolutely correct thickness for the counterbalance; the thickness thus found, although close enough for practical purposes, is only approximate, for the following reason : In the first place, we should have considered the counterbalance to consist of a number of segments fitted around the spokes and part of the rim, and then found the common center of gravity of these segments. Instead of this, we found the center of gravity of the whole counterbalance without making the proper allow- ances for the amount of metal which must be cut out of the counterbalance for the spokes and rim. Consequently the center of gravity G, as we have determined it, will be somewhat a very small amount too far away from the center i of the axle. Secondly, simply adding the weight of those portions of tlit- sjiokt-s and rim which are cut out for the purpose of making room for the counterbalance to the weight required for coun- 1i-rli;ilaiifing the weights applied to the crank-pin, is not quite correct. The exact procedure would be to find the common center of gravity of the portions cut out of tin- 250 MODERN LOCOMOTIVE CONSTRUCTION. wheel center, so as to obtain the correct distance between this center of gravity and the center of axle, aiid then find the amount of weight which, when applied to the center of gravity G of the counterbalance, will have the same effect as the weight of the portions of the spokes and rim, cut out of the wheel center, applied to their own center of gravity, and then add this weight, so found, to the weight required for counterbalancing the weights applied to the crank-pin. But such a course requires a great amount of labor, and may, on account of its complicacy, and the errors which may creep into it, give no better results than those obtained by the simpler method. 274. In ten-wheeled, Mogul, and consolidation engines, the weight of the recipro- cating parts which are to be counterbalanced is often equally distributed throughout the driving wheels, thereby making the counterbalances in all wheels, excepting the main wheel, equal in size. The counterbalance in the main wheel will, of course, be a little larger than the others, because it has to counterbalance a heavier crank-pin than those in the other wheels, and has also to counterbalance the weight of one-half of the connecting-rod, which the counterbalances in the other wheels have not to do. In some instances this arrangement will require in the main wheel a counterbalance whose thickness is too great to pass through the available space; consequently, in such cases, the total weights of the revolving and reciprocating parts are assumed to be equally distributed throughout all the wheels, and calculations of the counter- balance made accordingly, making the counterbalances in all the wheels (main wheel included) equal in size and weight. 275. Even with this arrangement, considerable difficulty is often experienced in the endeavor to obtain sufficient weight in the counterbalance for narrow-gauge locomotives having driving wheels of comparatively small diameter, say 3 feet. In fact, in many of these small wheels it is impossible to obtain sufficient weight with cast-iron, and therefore these counterbalances are frequently cast hollow and filled with lead for instance, such as is shown in Fig. 394. This figure represents Section throityh a b Fif/. 396 Fiff. 394 a wheel center 33 inches diameter, and is designed for a narrow-gauge (3 feet, or 3 feet 6 inches gauge) locomotive. Fig. 395 represents a section of the counter- balance through the line a b (Fig. 394), and, as will be seen, it is cast hollow, so that it may be filled with lead. We use lead because it is considerably heavier than cast- iron, and consequently we can obtain a counterbalance which will need less room MODERN LOCOMOTIVE CONSTRUCTION. 251 thaii a oast-iron counterbalance of the same weight. We are compelled to use a counterbalance of small dimensions, and yet a heavy one, because, on account of the small diameter of the wheel, the length of the arc x x 2 % (which is the length of the counterbalance) and also the depth a y are limited. The available space through which the counterbalance has to move will also limit the thickness d 2 e 2 in Fig. 395. Another fact we must not lose sight of, is that, occasionally, in small wheels, the distance between the center of gravity G of the counterbalance and the center of the axle will be less than the length of the crank ; consequently in cases of this kind the weight of the counterbalance will be greater than that applied to the crank-pin ; such conditions do not occur in large wheels. Small wheels leave us but very little choice in the length x x 2 x 3 of the counterbalance, which frequently must be extended around the wheel as far as we can possibly go with advantage. The choice of the width a y is also limited ; all we can do is to make it as wide as we can, leaving only sufficient room between the counterbalance and the hub, that is, between a and p, for oiling the axle journals when the counterbalance stands above the center j. 276. The thickness of this class of counterbalances can be determined by the following method, which saves labor and promotes simplicity, but will give only approximate results, though "close enough for practical purposes. EXAMPLE 82. The length of the crank is 9 inches; total weight applied to the crank-pin, which is to be counterbalanced, is 300 pounds ; it is required to find the thickness of the counterbalance. Make a drawing of the wheel center as shown in Fig. 394. Lay in the counter- balance, and let it extend from the center I m of the arm A to the center o n of the arm B. This length of the counterbalance is arbitrary ; an experienced designer will know that, under the conditions, it must be made as long as possible ; and anything beyond the lines I m and o n will add little, if any, appreciable effect to the counter- balance. Let us also decide to make the width a y equal to 6 inches; this will leave about as little room between a and p as we can get along with in oiling the axle journal. Let us now consider that our counterbalance is simply a cast-iron box whose cross-section is rectaugulai-, as represented by the lines d 2 f,, f 2 p 2 , p 2 e^ and d 2 e 2 , in Fig. 395 ; also let us consider that the cross-section of the lead is represented by the rectangle d efg 1i. Now the depth d 2 f 2 of the box is established, the thickness of the sides of this box is also established, which is to be of an inch. We may, therefore, find at once the weight of sides d 2 f 2 and e 2 p. 2 in the following manner : Midway between the arcs m a o and I y n draw, from the center,/, the arc x X 2 x 3 ; multiply the length of this arc by the depth a y, by the thickness of the side, and by the weight of a cubic inch of cast-iron ; the product will be the weight required ; thus : Assume that by measurement we find the length of the arc x X 2 X 3 to be 29 inches; then 29" x G" x 3" x .26 = 33.93 pounds, which is the weight of one side, and 33.93 x 2 = 67.86 pounds, which is the weight of both sides, d. 2 f. 2 and e 2 p 2 . Let us now assume that tho counterbalance is divided into a number of slabs, as indicated by the dotted lines </.,/ ,/ 4 / 4 , etc., each slab 1 inch thick, tin- divisions or cutting planes being parallel to the face I m a y o n of the counterbalance. Let us now find the weight of one of these slabs. Each one of them is composed of two kinds of metal, namely, lead and cast-iron. Of course, lead predominates. The 252 MODERN LOCOMOTIVE COXSTBVCTIOJf. weight of lead is generally reckoned at 0.41 pound per cubic inch. Consequently the area bounded by the dotted lines r s, t u, and the arcs s v t, r iv u, multiplied by .41, will give the number of pounds of lead in one slab. The area of this surface of lead is found by multiplying the length of the arc # 4 2 % by width v w. The width v ic is, under the given conditions, equal to 4 inches ; and assuming that by measurement we find the length of the arc # 4 x 2 X 5 equal to 27J inches, we have for the weight of lead in one slice, whose thickness is 1 inch, 27" x 4" x .41 = 50.7375 pounds, say 50IJ pounds. To this weight must be added the weight of the cast-iron included by the arcs m a o and s v t ; also that between the arcs r w u and I y n, all 1 inch in depth. Let us assume that we have found by calculation the weight of this amount of cast-iron to be equal to 10 pounds, then the total weight of one slab will be equal to 503 + 10i = 61 pounds. Cut a templet to conform to the outline I m a o n y of the counterbalance, and find its center of gravity G by the method shown in Fig. 385 ; lay off this center of gravity on the drawing, and measure its distance from the center j of the axle ; this distance, we will say, is equal to 8 inches. The moment of the force due to the weight applied to the crank-pin is equal to the product of the length of the crank into the weight applied to the pin ; hence we have 300 x 9 = 2700. The moment of the force due to the weight of the counterbalance is also equal to 2,700 ; hence the total weight of the counterbalance must be equal to 2700 --T = 317.64+ pounds. o.O But we have already found that the weight of the two cast-iron sides d 2 f 2 and e 2 p. 2 (Fig. 395) is equal to 67.86 pounds. Subtracting this weight from the total weight of the counterbalance, we have 317.64 67.86 = 249.78 pounds. This weight of 249.78 pounds must now be made up by the weight of the slabs into which the counterbalance has been divided. Therefoi'e, we must now find the number of slabs required to make up the weight of 249.78 pounds. Since we have found that the weight of each slab is equal to 61 pounds, we have 249.78 ^i = 4.09, say 4 slabs. And lastly, since each slab is 1 inch thick, the thickness of the lead from d to e must be 4 inches, and the total thickness from <7 2 to e 2 of the counterbalance must be equal to 4 + l = 5J inches. In this case we have left out the weight of the arms and rim, which must necessarily be cut out of the wheel to insert the counterbalance, but this weight is generally made up by filling the opening y h i k with lead. 277. Figs. 396, 397 represent a 42-inch wheel center with lead counterbalance, designed in one of our prominent locomotive works. It is suitable for heavy freight engines with cylinders 20 inches diameter and up to 22 inches. Mi>ltKR\ LOCOMOTIVE COXKTRVCTION. 253 Figs. 398, 399 represent a driving wheel with lead counterbalance. It is used on elevated railroads. We believe that in this wheel the arms and rim could have been made lighter, and still be strong enough to do excellent service. counterbalance '\ 254 MODERN LOCOMOTIVE CONSTRUCTION. 278. In locomotive construction we have sometimes to find the areas of plane surfaces or figures similar to that shown in Fig. 400. The area of such a figure may be found in the following manner : Divide the line a I into any number of equal parts, say five, and through the points of division c, fj, /, k, draw lines perpendicular to a I terminating in the curve c h d. The lines ef, g h, etc., are called ordinates, and for the sake of simplicity we r Q p t . *< 4 r- i d I- , Fiy. 400 Fig. 403 may also consider the lines a c and b d to be ordinates, although in reality they are bounding lines of the plane. Let P, P.,, P 3 , P 4 , P 5 , P 6 represent the lengths of the ordinates, and s the distance between any two successive ordinates that is to say, s = e g or g i. The area of this figure may then be found by the following : RULE 51. To find the area between a given curve and a straight line, such as c h d and a b in Fig. 400. To one-half the lengths of the extreme outer ordinates add the length of all the intermediate ordinates, and multiply the sum by the distance between any two successive ordinates ; the product will be the area. Or, putting this rule in the shape of a formula, we have (i P + Pz + P^ + P^ P r> + J P 6 ) x s = area. EXAMPLE 83. Suppose we find the length of a c equal to 2& inches, ef=3,gh = LOCOMOTITE COXSTRVCTJOX. 255 2 );:, / j = 2,^., i- i = 2-jij,., b d = 2, and the distance ,s between any two successive ordinates equal to 1J inches ; it is required to find the area. 97 // 2"\ -f- 4- 3" + 2ii" + 2-jV' + 2iV + ^-j x 1J" = 16| square inches. The accuracy of the result depends on the number of ordinates ; the greater the number, the greater the accuracy. In the next article we will give practical applications of this rule. 279. In a number of locomotives the outer foi m m of the rim of the driving wheel is uniform throughout. Such a wheel is shown in Fig. 358. There we notice that a portion of the rim, opposite to the crank, is cast solid, and the remaining portion of the rirn is cast hollow. But, in many cases, the extra weight of metal gained by casting part of the rim solid is not sufficient for counterbalancing the whole weight applied to the crank-pin ; consequently we often find the whole rim cast hollow, and of equal dimensions throughout, with a certain portion of the rim opposite the crank filled with lead, so as to obtain a greater weight in the same amount of space than can be obtained by casting a portion of the rim solid. Hence, it frequently happens that the weight of the lead in the rim, and its effect as a counterbalance, must be calculated. Let Fig. 401 represent a part of a driving wheel whose rim is cast hollow, and of uniform cross-section throughout. The section around the center line b c represents a cross-section of the rim ; and Fig. 402 represents the same section on a larger scale. The portion of the rim from the rib a to the rib 6 is filled with lead. It is required to find the weight of the lead, and its effect as a counterbalance; that is to say, to determine the amount of weight applied to the crank-pin which the lead in the rim can counterbalance. This problem includes two distinct problems, namely, to find the weight of the lead ; second, to find the effect of the weight of the lead as a counterbalance. For the sake of simplicity we shall leave the ribs 3 , 4 , a 6 which are cast in the rim out of consideration, and proceed as if the hollow part of the rim from the rib a to the rib a 6 had been a clear space and then filled with lead. WEIGHT OF THE LEAD IN THE BIM. In looking at this counterbalance, or body of lead, from a theoretical standpoint, we may consider this body or solid to be generated by a surface which is equal in extent to the cross-section of lead revolving about the center of the axle, and this surface we may call the generating surface. The contents (that is, the number of cubic inches) of this solid is obtained by multiplying the area of the generating surface in square inches by the length of the path (or arc, in this case) in inches described by the center of gravity of the generating surface ; the product will be the number of cubic inches in the cotmterbalance. And lastly, the number of cubic inches multi- plied by the weight of one cubic inch of metal will be the weight of the counterbalance. Consequently we have the following : RULE 52. Multiply the area in square inches of the cross-section of the lead by the length of the arc in inches, described by the center of gravity of this cross-section ; the product will be the number of cubic inches in the counterbalance. This last 256 MODERN LOCOMOTIVE CONSTRUCTION. product, multiplied by the weight of one cubic inch of lead, namely, .41 pound, will be the weight of the counterbalance. From the foregoing we see that in determining the number of cubic inches in the counterbalance two distinct factors enter into our calculation, namely, the area of the cross-section of the lead, and the length of path which the center of gravity of this section will describe. The outline of the cross-section of the lead is represented by the outline d e h c n kj of the cavity in Fig. 402. The area of this cross-section can be found by Rule 51. Thus : Draw the line I c perpendicular to p r. If the outline of the section is symmetrical, the line b c must be drawn through the center of the section ; if the outline of this section is not symmetrical, we first draw a line s t (any length) parallel to line p r, and touching the curve i c o in one point, as c, and then through this point, that is, the point of tangency, draw the line b c perpendicular to p r, as before. Let us assume that the outline of the section is symmetrical. Through the point e draw a line e e z perpendicular to the line I c. Divide the distance from e., to c into any number of equal parts, say five ; through the points of division f 2 , g 2 , h. 2j and i 2 draw lines perpendicular to b c, cutting the outline of the section in the points /, c/, h, i. Suppose now that we find, by measurement, the line e e 2 to be equal to f inch ; ff 2 = 1& ! 9 9i = 1 5 '* lh = i 5 * *2 = 8 ; and c of course = ; also, the distance, such as f 2 g. 2 , or g 2 h 2 , that is, the distance between any two successive ordinates or perpendicu- lars, equal to ^ 6 - inch. The area of the surface e 2 c life will then, according to Rule 51, be equal to 3" \ ~ + 14" + 1" + I" +' S" + f ] X J\, = 2.32+ square inches. To this we must add the area of the rectangle b d e e. 2 ; and since b e 2 is equal to inch, and e e 2 = inch, we have .875 x 75 = .65+ square inch; hence 2.32 + .65 = 2.97 square inches, which is the area of the section above the line b c ; and 2.97 x 2 = 5.9 square inches, the total area of the cross-section of the lead. If the outline of the section is not symmetrical, as we have assumed it to be, then we find area of the surface above the line b c, and that below the line b c, each one separately, in a manner precisely similar to the foregoing, and add the two together ; the sum will be the total area of the surface. Our next step will be to find the length of the path described by the center of gravity of the cross-section of the lead. Cut a templet to the outline d c h c n kj of the cavity (Fig. 402), and find its center of gravity G by the method shown in Fig. 378, and mark this point G in its correct position from b in the section shown in Fig. 401. From the center of the axle describe an arc passing through the center G, and terminating in the sides of the brackets a and a & . This arc will repi'esent the path of the center of gravity G of the cross-section, while this cross-section, or generating surface, is revolving about the center of the axle. Now suppose that, by measurement, we find the length of this arc from a to a 6 to be 57 inches, then the total number of cubic inches in the lead will be equal to the product obtained by multiplying the area in square inches of the cross-section, previously found, by the length in inches of the arc a 4 a 6 ; hence we have 5.9" x 57" = 336.3 cubic inches. Multiplying the cubic VODER* LOCOMOTIl'K COXSTRCCTJOX. 257 inches by the weight of one cubic inch of lead, we have 336.3 x .41 = 137.883 pounds, which is the total weight of the lead in the i'im. EFFECT OF THE LEAD COUNTERBALANCE IN THE RIM. 280. Our next step will be to determine how much of the weight applied to the crank-pin will be counterbalanced by the weight of the lead in the rim. To do this we must find the center of gravity G., (Fig. 401) of the whole amount of lead, and the correct distance between this center of gravity and the center of the axle. But here a little difficulty arises ; we see that the thickness of the lead is not uniform, that is to say, the lines k e, If, m g, etc., in the cross-section of the lead, as shown in Fig. 402, are not equal in length ; therefore we cannot find the center of gravity of the lead by the method shown in Fig. 385, or by any method previously given ; hence we adopt the following method : In the first place we shall assume that the area of the cross-section of the lead is infinitely reduced, so that the whole counterbalance will be represented by the arc a m ffl 6 (Fig. 401), which is described from the center of the axle and passes through the center of gravity G of the cross-section ; and we shall also assume that the whole weight of the lead is concentrated along this arc, or, in other words, the weight of this arc o m 6 is equal to the whole weight of the lead. Join the extremities a and fi of this arc by a straight line, which will be the chord. We have now reduced the condi- tions of the problem to those of a very simple one, for we have now only to find the center of gravity of the arc a m a 6 . In J. Weisbach's " Theoretical Mechanics " we find that the center of gravity of an arc of a circle must lie in the radius drawn through the middle of the arc, because this radius is an axis of symmetry of the arc ; consequently in our problem the center of gravity G. 2 of the arc a m a 6 must lie in the line n m, which is drawn through the middle m of the arc to the center of the axle. Again, we find that the distance from the center of gravity of the arc to the center from which the arc has been described is to the radius of the arc as the chord is to the arc. To indicate these proportions by symbols, let Length of the arc be represented by ........................................ b Length of the chord " " ........................................ s Length of radius " " " ........................................ r Distance of center of gravity " " ........................................ y Then we have y : r : : s : b. Consequently, s r From the foregoing we can establish the following rule : RULE 53. To find the center of gravity of the lead in the rim, multiply the length in inches of the chord joining the extremities of an arc which is described from the ci-nter of the axle and passing through the center of gravity of the cross-section of the lead by its radius in inches, and divide this product by the length of the arc in inches; 258 MODERN LOCOMOTIVE CONSTRrCTIOX. the quotient will be the distance from the center of the axle to the center of gravity of the arc. We have already seen that the length of the arc a m a 6 is 57 inches ; now suppose we find by measurement that the chord a a G is 48J inches, and the radius 29 inches, then the distance of the center of gravity G 2 of the lead in Fig. 401 from the center of axle will be equal to 48.5" x 29.5'^ 57" = 25.1 inches. We have found that the weight of the lead is 137.883 pounds, consequently the moment of the force due to the weight will be equal to 137.883 x 25.1 = 3460.86+. If we now assume that the length of the crank is 12 inches, then our lead will counterbalance a weight applied to the crank-pin equal to 3460.86 = 288.4 pounds. WEIGHT OF CRANK-PIN HUB. 281. In Art. 254 it was shown that, in order to determine the amount of weight required to counterbalance the weight of the crank, we must first find the center of Fig. 4O4 gravity of the crank. In Art. 270 it will also be seen that, on account of the difficulty of determining accurately the center of gravity of the crank, many draftsmen and engineers will often, instead of counterbalancing the weight of the crank referred to the crank-pin, content themselves by simply adding the weight of the crank-pin hub to the other weights applied to the crank-pin, and then counterbalancing the sum of MOHKRX LOI-it.MOTJI'K <;O\XTIircTI(>\. 259 weights. Hence the question may arise: How can we find the weight of the mink-pin hub? The weight of the craiik-j>iu hub can be determined by the same method and rules which were employed for finding the weight of lead in the rim of a wheel, as explained in Art. 279. Thus, for instance : Let Fig. 403 represent the longitudinal section of the crank-pin hub whose weight we are to determine. We first find the area of the section of the metal / m n o p. To do this we follow Rule 51. Therefore, divide the distance n p into any number of equal parts, and through the points of division draw lines perpendicular to the line n p, terminating in the curve m I o. Let A, B, C, etc., represent the length in inches of the perpendicular lines (the lengths being obtained by measurement). Then, according to Rule 51, \-z + B+C + D + E + aj x s = area in square inches. We must now find the center of gravity G of the surface I m n o p. To do this, cut a templet to the outline of this surface, and find its center of gravity by the method shown in Fig. 377. Mark off this center of gravity G on the section of the hub, and measure its distance G h from the center line i k ; twice the distance G h will be equal to the diameter of the circle whose circumference will be the path of the point G as the surface I m n o p revolves around the center line i k. According to Rule 52, the number of cubic inches in the hub will be equal to the product obtained in multiplying the circumference in inches of the circle described by the center of gravity G, by the area in square inches of the surface I m n o p. This last product, multiplied by the weight of one cubic inch of cast-iron (.26), will be the weight of the crank-pin hub. DRIVING WHEEL TIRES. 282. At present, nearly all driving wheel tires are made of steel. The most common practice is to shrink the tires on the wheel centers, as explained in Art. 248. When tires are to be shrunk on, they are bored out to a uniform diameter throughout, so that their sections will appear like that shown in Fig. 404. Of course the inside diameter of the tire must be a certain amount less than the diameter of the wheel center ; care must be taken not to allow too much for shrinkage, as this will draw the tire too tight, and will be liable to burst it when the engine is running; on the other hand, with an insufficient allowance for shrinkage, the tire will, in a short time, become loose; the shrinkage diameters adopted by the American Railway Master- Mechanics' Association are given in Art. 248. 283. When steel tires are properly shrunk on the wheel centers in this manner, they will remain tight and resist all the lateral thrust caused by the flanges bearing against the rails, until they are worn considerably. Then these tires need watching, as the constant rolling action is liable to loosen them. When this is the case, shim- ming pieces are often placed ltd ween the tires and wheel centers. Occasionally the excellent plan as shown at A in Fig. 404 is adopted. Here it will be seen that a slight projection or flange is left on the periphery of the wheel center near its inner face, or flanged side of the wheel. Tin- purpose of this design is that the projection shall the thrust caused l.y the flanges bearing against the rails, and prevent the 260 MODERN LOCOMOTJfE COXSTRVCTION. tire from slipping inward should it at any time become loose. Yet it seems that the general inclination is to avoid the extra expense incurred in putting the tires on the wheel centers in this manner, and consequently the most common practice is to bore out the tires straight. 284. Very seldom do we find tires which have not been shrunk on, but placed cold on the wheel centers ; in fact, we know of only one road in the United States Kim of Wheel Centre Arm I Fig, 406 where this practice prevails. On this road the tires are bored out, tapered, and the periphery of the wheel center turned to suit, as shown in Fig. 405. The large diameter of the bore of the tire is on the flanged side, or, in other words, on the inside of the wheel. The tire is prevented from slipping outward by the hook-headed bolts B. The taper prevents the tire from slipping inwards, and resists the thrust caused by the flange bearing against the rails. Eight hook-headed bolts B are gen- erally used for a tire 63 inches inside diameter ; and six bolts B for a tire 35J inches inside diameter. The nuts on these bolts are not allowed to project beyond the inside of tire ; consequently, recesses for the nuts are cast in the rim of the wheel center ; another view of one of the recesses, and metal partially surrounding it, cast to the rim, is shown in Fig. 406. The advantage claimed for this mode of putting tires on the wheel centers is that they can be removed when necessary with less labor and delay than will be required for removing tires which are shrunk on the wheel centers, and also, should the constant rolling action loosen the tires at any time, they can be quickly tightened. We decidedly prefer the tires shrunk on wheel's center, as we believe that, with these, safety is promoted and better results obtained. 285. In fitting up a pair of driving wheels, the wheel centers are first pressed on the axles with a pressure equal to that given in Art. 252. The keys are then driven, and the tires shrunk on. After this the wheels and axle are placed in a quartering machine and the holes bored for the crank-pins. It is very important to have the crank-pins exactly in line with the axle, and at equal angles in all the different driving wheels, and such results are obtained in a correctly designed quartering machine. The crank-pins are then pressed into the wheel centers with a pressure of about MODERN LOCOMOTIVE CONSTRUCTION. 261 six tons for every inch in diameter of the crank-pin fit, providing the holes are perfectly true and smooth. If the holes are not perfectly true, which may not only be due t<> liad workmanship, but may be, and sometimes is, the result of the bad practice of shrinking the tires on the wheel centers after the crank-pin holes have been bored, a pressure of nine tons per inch in diameter is necessary for pressing the crank-pins into the wheels. The last operation is to turn the tires to the correct gauge. CLEARANCE BETWEEN FLANGES AND RAILS. 286. The tires are placed on the wheel centers so as to allow a certain amount of clearance, C (Fig. 404), between the flanges and the rails. The most common amount of clearance allowed at C for each wheel is f of an inch, making the total clearance between the rails and the flanges of a pair of driving wheels inch. On a few roads this clearance for each wheel is only \ inch, and, on the other hand, we occasionally find it increased to J inch. We are in favor of inch clearance for each wheel. Should the distance between the rails of a curve be established, and any doubt exist as to the sufficiency of this amount of clearance in running over the curve, the proper amount of clearance can readily be obtained by making a plan of the cui-ve, and also a plan of the wheels with the correct distances between the axles drawn upon the former ; the distance between the flanges of a pair of driving wheels can then be regulated to allow a necessary amount of clearance, which will prevent the wheels from binding in running over the curve. PLAIN TIRES. 287. Fig. 407 represents a cross-section of a tire without a flange ; tires of this kind are generally called " plain tires." These tires are generally wider than the flanged tires under the same engine. The width of the plain tires must be made to suit the curves over which the engine has to run, and should be sufficiently wide not to leave the track at any time. To determine this width, a plan cj-r of the curve and wheel base must be made, and t "- + - " Fig. 4O7 the width of the plain tire regulated so as to cover the rails at all times. As a consequence, the width of the plain tires varies, under the different classes of engines, from 5 to 7 inches. DISTRIBUTION OF FLANGED TIRES IN THE VARIOUS CLASSES OF LOCOMOTIVES. 288. In a large majority of eight-wheeled passenger engines, in which four of the whole number of wheels are driving wheels, as shown in Fig. 1, all the driving wheels have flanged tires. We have noticed only a very few of this class of engines in which one pair of drivers the front ones had plain tires, leaving only one pair of driving wheels the rear ones to guide the engine over a curve. This we believe to be dan- gerous practice. All wheels in this class of engines should have flanges. 262 MODERN LOCOMOTIVE CONSTRUCTIVE. In a great number of Mogul engines, in which six wheels of the whole number are driving wheels, as shown in Fig. 2, the front and rear driving wheels have flanged tires ; the middle pair have plain tires. We believe this to be the best practice, for the following reasons : All locomotives have a tendency to sway in front from side to side; this is objectionable. Now, a Mogul engine has only a two-wheeled truck (generally called a pony truck) in front, and such a truck without the aid of the flanges on the first pair of drivers is not suitable to guide the engine steadily on a straight track, neither is it suitable to guide it safely over a curve. In short, more than two wheels with flanges (particularly when these wheels are truck wheels) are needed to guide the engine steadily in front. In ten-wheeled engines, in which six wheels of the whole number are driving wheels, as shown in Fig. 3, the rear pair of drivers, and the pair next to it, have flanged tires. In these engines the four-wheeled truck in front is generally considered to be sufficient to guide the engine . steadily on a straight track and safely over a curve without the aid of flanges on the front driving wheels. In consolidation engines, in which eight wheels of the whole number are driving wheels, as shown in Fig. 4, the distribution of flanged tires somewhat differs on the various railroads. All these engines have in front a two-wheeled that is, a pony truck, and since, as we have stated before, a two- wheeled truck is generally considered insufficient to guide an engine steadily on a straight track or safely over a curve, we find that nearly every engine of this class has flanged tires on the front drivers. As to the other driving wheels under the same engines, we often find the rear pair, and the pair next to it, with flanged tires, leaving only one pair of driving wheels (the pair next to the front ones) with plain tires. This arrangement seems to indicate that some designers consider two pairs of the whole number of wheels, including truck wheels, to be necessary for the pur- pose of guiding the rear end of the locomotive, and two pairs of wheels to guide the front end. But this arrangement is by no means a universal one, as we frequently meet with consolidation engines in which only the rear and front pairs of driving wheels have flanged tires, leaving the two intermediate pairs of driving wheels with plain tires. This arrangement seems to indicate that if one pair of wheels with flanges is sufficient to guide, as is generally the case, the rear end of a Mogul engine, one pair of wheels with flanges will also be sufficient to guide the rear end of a consolidation engine, and that plain tires on the two intermediate driving wheels will allow the engine to curve easier. In a few instances we find the flanged tires distributed so as to bring the flanges on alternate driving wheels. In such cases the rear and third pair of driving wheels, counting from the rear end, will have flanged tires, the second pair from the rear and the front pair will have plain tires. Our favorite arrangement is to have flanges on the front and rear driving wheels ; these, we believe, will guide the engine steadily, and allow it to curve easily. Lastly, occasionally we meet with consolidation, Mogul, and ten-wheeled engines under which all the driving wheels have flanged tires. MODERN LOCOMOTIVE CONSTRUCTION. 263 DEPTH OF FLANGES. 289. The depth D E of the flanges of tires (Fig. 408) varies, according to the ju< lament of the designer, from 1 to 1J inches; and in a few instances the flanges are made l inches deep, as shown in Fig. 405. Many master-mechanics claim that flanges 1 inch deep are perfectly safe, and to prove their assertion point to engines with fcsJH flanges 1 inch deep on the drivers which are and have been running daily without any trouble or accidents ; yet others claim that flanges l inches deep are safer, and adopt this depth for all their driving wheel flanges. In a large majority of locomotives the driving wheel flanges are l inches deep an arithmetical mean of 1 and 1|. FORMS OF TREAD ON DRIVING WHEELS. 290. At present various forms of tread on driving wheels are used. Fig. 408 represents a section of a tire in which the tread a b is a surface of uniform taper. This taper varies on the different roads from to | of an inch in 12 inches. This form of tread is usually called the cone tread. Fig. 409 represents a section of a tire in which the tread is composed of two surfaces; one surface is represented by the line c rf, and is turned to a uniform diameter ; the other surface is represented by line d e, and is turned to a uniform taper ; in some cases this taper is as much as J of an inch in 1J inches. This form of tread is often called the straight tread. Fig. 410 represents a section of tire in which the tread is also composed of two surfaces, fg and g h. The surface fg is turned to a slight taper, as shown ; and the surface g h is turned to a greater taper, whose dimensions are also given. This form of tread is a modification of the cone tread, and its advantages will be presently explained. BEST FORM OF TREAD. 291. The question now arises : Which is the best form of tread for locomotive tires I We have already seen that all locomotives have a tendency to sway from side to side at the front end, and such a sinuous motion is objectionable. Tires with a cone tread, as shown in Fig. 408, will certainly reduce to some extent this objection- able sinuous motion. We may therefore claim for the cone tread, particularly in engines which have only a pony truck to guide the front end, and where some depend- ence must be placed on the front drivers to guide, in some measure, the engine steadily, that the cone tread will help to keep the engine in the center of the track, 264 MODERN LOCOMOTIVE CONSTRUCTION. and to some extent reduce the wear on the flanges. True, the taper of the tread near the base of the flange will soon wear off, and a channel or groove in the tire will be formed, as shown in Fig. 411. In this case the form of the ridge near the flange will, to some extent, answer the same purpose as that for which the cone tread was originally designed. Hence we may say that the cone tread is particularly desirable for engines in which the tires are new, or have not been worn. Indeed, this fact has often been proven by experience on roads, and more distinctly so on roads with sharp curves, where straight treads had to be abandoned and replaced by cone treads, so as to obtain more satisfactory results, cause the engine to run with greater safety over the curves, and reduce the wear of the flanges when new. On the other hand, the claim that a cone tread will cause the engine to run over a curve with less friction and less wear on the tires than with treads of other forms is a fallacy. For instance, the argument that the centrifugal force will cause the engine to run towards the outer rails of a curve, and thus cause the outer driving wheels to work on their large diameter and the inner driving wheels to work on their small diameter, thereby creating a rolling motion similar to that of a cone on a flat surface, cannot be sustained when sound principles are applied. It is true that when a single cone is rolled over a flat surface it will run in a curve whose radius is dependent on the taper of the cone. But if we now take two equal cones and fix their axes rigidly and parallel to each other in a frame, so as to obtain conditions similar to those of parallel axles and wheels under an engine, and then roll the cones over a flat surface, the results thus obtained will greatly differ from the results noticed in rolling one of the cones separately. The two cones thus held together will roll in a curve which approaches a straight line ; considerable sliding friction will also be created, so that the forces required for rolling both cones held together will be considerably greater than the sum of the two forces required for rolling each cone separately. The claim that the centrifugal force will cause the engine to run towards the outer rails of the curved track is also very doubtful, because, to obtain such a result, the radius of the curve would have to be suitable for the speed of the engine, or the engine would have to be run at a speed suitable for the radius of the curve, and these are conditions which cannot be obtained in practice. Hence we conclude that the cone tread will not lessen the wear or friction on the tires in running over a curve, but it has this advantage, that it will generally prevent, to some extent, the sinuous motion of the locomotive, and that on this account it will somewhat lessen the wear of the flanges. The tread shown in Fig. 410, and treads similar to it, have in late years greatly grown in favor ; and we believe these to be the best to adopt, as they possess not only the advantage of the cone tread, but, furthermore, possess the advantage of wearing to a better form than the cone tread, because the increased taper of the tread near the edge of the tire will reduce the outer ridge of the groove or channel shown in Fig. 411, the groove being always an objectionable feature. The straight tread shown in Fig. 409 possesses only the advantage of wearing to a form approaching that of Fig. 410, but it does not possess the advantage of steadily guiding the engine when the tires are new. MODERX LOCOMOTirE COXSTKVCTION. 265 92. In the Proceedings Twentieth Annual Convention, 1887, of the American Railway Master-Mechanics' Association, we see it reported that the form of the tread, such as shown in Fig. 412, has been adopted as a standard, which is the same form of Ml v -X-* ^^ '-;' -i ;;- x4 = - \ ~ ^ -^ i. ^ ** ir r^j," 1 Fig. 412 tread as that adopted by the Master Car Builders' Association, and has been illustrated in the report of their twenty-first annual convention, from which our illustration has been taken. Figs. 409, 410, and 411 have been taken from the report of the proceed- ings of the seventeenth annual convention of the American Railway Master-Mechanics Association. THE LIMIT OP WEAR OF TIBES. 293. A fixed limit to which the thickness of a tire can be reduced by wear without impairing the safety of running the engine cannot be established, as the weight on the drivers, the climate, and quality of the steel will have some influence on the limit of wear. But generally, experience seems to indicate that in warm climates tires made of good homogeneous steel may remain in use until their thickness has been reduced to 1J inches ; for light engines, whose weight does not exceed 10,000 pounds on each driver, the tires may remain in use until their thickness has been reduced to li inches. In colder climates, although sometimes we there see engines running with tires reduced to 1J inches in thickness, we believe that safety will be promoted by removing the tires before this limit has been reached. THICKNESS AND WIDTH OF TIRE. 294. On many roads the thickness of the tire when new is 3 inches, measured at the base of the flange as indicated by the dimension line in Fig. 408. On some roads this thickness has been considerably increased, so that we now find many loco- motives with tires 4 inches thick. The advantage claimed for thick tires is that they will, to some extent, reduce the expense of keeping the engine in working order, because, generally, tires, of whatever original thickness, are not allowed to wear below a thickness of 1J inches, and are then taken off the wheel center; consequently the interval between the renewals of tires 4 inches thick will be greater than the interval between the renewals of 3-inch tires, and thereby time and labor are saved when the former thickness has been adopted. Attain, the amount of steel tin-own away, so to speak, when the tire is condemned on account of its reduction, will, in comparison witli the original weight of the tire, be less for tires 4 inches thick than for those whose original thickness was below 4 inches. On the other hand, with the use of heavy 266 MODERN LOCOMOTIVE CONSTRUCTION. tires a greater dead weight than desirable, that is to say, a weight not supported by the springs, is placed on the rails, and such a procedure must in time injure the rails It is therefore probable that in the future the thickness of tires will not exceed 4 inches. The width of flanged tires generally varies from 5 to of inches. DISTANCE BETWEEN THE BACKS OF FLANGES ON TIBES. 295. It is important that the distance between the backs of flanges on tires should be suitable for the gauge of the road on which the engine has to run. Increasing this distance will obviously decrease the thickness of the flanges, which is not desirable. Decreasing the distance between the backs of flanges beyond a certain limit will interfere with the guard rail on the different lines of railroads. For a gauge of 4 feet 8J inches the distance between the backs of flanges is generally made 4 feet 5g inches. On a few roads we find this distance decreased to 4 feet 5J inches ; and on some other roads increased to 4 feet 5J inches. CHAPTER VII. MAIN-RODS. SIDE-RODS. CRANK-PINS. MAIN-RODS AND SIDE-RODS. 296. Figs. 413, 414 represent a main-rod, and Figs. 415, 416 represent a side-rod. Both were designed for a four-wheeled connected engine, such as shown in Fig. 1, cylinders 17 x 24 inches. The office of the main-rod is to transmit motion from the crosshead to the main drivers ; it connects the crosshead pin and the main crank-pin, and therefore is somo- tinies called the connecting-rod. The term main-rod is mostly used in this country, and will be adopted in the following descriptions. The office of the side-rod is to transmit motion from the main driving wheels to the other driving wheels ; it forms a connection or coupling between the drivers, and therefore is sometimes called a coupling-rod ; or again, because the side-rod on one side of the engine is always parallel to the side-rod on the opposite side, it is some- times called the parallel-rod. But the term side-rod is by far the most popular one, and will be adopted in these articles. Several different designs of main- and side-rods are in use, as will soon be shown ; but the designs here represented, we believe, are the most common ones for the class of engine named. The end of the main-rod marked F, Fig. 413, is usually called the front end ; and the opposite end, marked i?, the rear end. The design of the front end of a main-rod depends on the kind of crosshead to be employed. The design of the front end F shown in Fig. 413 is only suitable for the class of crossheads shown in Figs. 234 and 237. 297. In both rods the number of bolts e e e required, and their diameters, for holding firmly the straps a a to the butt ends of the rods, depend on the magnitude of the forces which these rods have to transmit. In side-rods we generally find two bolts through each strap to be sufficient ; but in main-rods sometimes more than two bolts through each strap will be required. The manner of determining the number of bolts in the main-rod and the diameters of bolts through all rods will be explained hereafter. These bolts are generally turned to a taper of J inch in 12 inches ; that is to say, the difference of the two diameters 12 indies apart is J of an inch; sometimes this taper is only V,, inch in 12 inches. These bolts must have an exti-emely good fit in, and be driven tight into both the straps and butt ends of the rods; the object of the taper is simply this, that when it becomes necessary to refit the brasses 268 MODERN LOCOMOTIVE CONSTRUCTION. b b b, the bolts can be readily driven out without impairing or upsetting their ends. Another advantage of the taper is that, should these bolts at any time become somewhat loose, they can to some extent be quickly tightened by turning a small amount off the under side of the head. Each one of these bolts should have two MOHEliX L0( -OMO Tll'K < 'O.Y.N Tit I'C na\. 269 nuts, mid since these nuts are always placed at the under side of the strap, greater security should be provided by inserting split pins at the ends of the bolts. _!tS. The keys are nearly always made of steel. Main-rods have generally one key at each end ; in the design shown in Fig. 413, the key is placed at the back of the crosshead pin, and the key in the opposite end of the rod is placed at the back of the main crank-pin. This is good practice, as, with this arrangement of keys, the brasses / \ - ,** t* *"/ E8-* Lu fe tPPHl^t- >j l^-vwjft ^) T* I rfM r l i li "f" JT'TT 71 "'-' \^\^l^ fff-P E 270 MODERN LOCOMOTirp; CONSTRUCTION. can be adjusted to some extent, without perceptibly altering the length of the main- rod. Yet this arrangement of keys is by no means a universal practice, as there are many main-rods with the key at the front of the crank-pin, and one at the back of the crosshead pin. With this arrangement the rod will be lengthened when the keys are driven further into the straps. Side-rods, designed for four-wheeled connected passenger engines, generally have two keys through one end, and one key through the opposite end ; and indeed, for this class of engines this arrangement of keys gives satisfactory results. But in other classes of engines we sometimes find side-rods with two keys at each end, as will presently be shown. The taper of the keys in all rods varies from g to 1J inches in 12 inches. In many engines the small end of the key is threaded, passed through the guard d d, Fig. 415, and by means of the nuts on each side of the guard prevented from slipping out of position. In other engines we find the keys held in position by small set screws tapped into the straps or the rod, as the case may require, and for greater security, so as to prevent the key from flying out should the set screw at any time become loose. a split pin is inserted at the small end of the key. Liners are inserted between the keys and the brasses. The object of these liners is to prevent the keys from indenting or cutting the soft surface of the brasses. These liners are generally made of steel, sometimes of wrought-iron. Their thickness varies from \ to f inch. 299. Figs. 417, 418 represent a main-rod, and Figs. 419, 420 represent a side-rod for a four-wheeled connected engine, such as is shown in Fig. 1 ; cylinders 18 x 24 inches. The design of the main-rod is similar to that shown in Figs. 413, 414, with the exception that the keys (Fig. 417) are. plain and are held in position by set screws. The design of the side-rod, Figs. 419, 420, differs greatly from that shown in Fig. 415. As will be noticed, straps are not used for this side-rod. These rods are forged in one piece, the ends bored out, and brass bushings pressed in. The cross-section of the rod here represented also differs greatly from that of the ordinary side-rod. The cross-section of an ordinary side-rod is rectangular, similar to that shown at A, Fig 417, whereas the cross-section of the rod, Fig. 419, has the appearance of an I. There is another distinct type illustrated in Art. 301, thus giving three distinct types of side-rods which at present are in use. The advantages claimed by their respective advocates will be considered later. 300. Figs. 421 and 422 represent a main-rod strap with key. This form of strap is very often used ; in fact, in the majority of locomotives we find the straps on all the rods, excepting those on the front end of the main-rod, made to a rectangular form, as shown in our illustration. As to the strap on the front end of the main-rod, we are often compelled to round off its end as shown in Fig. 417, so as to give the strap sufficient clearance in the crosshead while the rod oscillates on the crosshead pin. The length c d of the space, or that part of the opening of the strap marked A, should be sufficiently great to admit the brasses and the liner / as shown. The length d e of that part of the opening marked 7? is determined by the number of bolts through the strap and the width of the key, as will be presently explained. LOCOMOTIVE CONSTRUCTION. 271 We occasionally meet with straps whose openings are of equal width throughout ; that is to say, the distance between t and t. 2 is equal to that between s and s 2 . But we believe it is safe to say that, in a large majority of straps, the thickness of the metal at / is greater than the thickness at g ; thus making the width s s 2 less than the width of the opening at t t 2 . The straps are planed so as to make the surface t paral- lel to t. 2 ; and s parallel to S 2 , leaving a projection in line with d. Since the por- tion of the strap marked g is weakened by the bolt holes i t, we may be led to the conclusion that this strap is badly proportioned, and such a conclusion will be correct, if only the strength of the strap is considered. Indeed, if we are required to design a strap which shall be simply of equal strength through- out, we would make the thickness at g greater than that at/ so as to allow for .*-> <K I HEU s A (I e B Fig. 421 *t tf *l 1 u the loss of strength caused by the holes / /. But in designing straps for locomo- tive rods, other considerations must be taken into account. One of the aims of a locomotive designer is to design an engine which can be kept on the road in good working order at a rnininmm cost, and also reduce as much as possible the time during which the engine is kept out of service for the nec- essary repairs ; and these are the conditions kept in view, or which should be kept in view, when a strap for a locomotive rod is to be designed. Consequently, the thickness of the straps at /is greater than at g for the following reason : In practice it is found that the inner surfaces * >s 2 will wear unevenly, and the brasses become loose long before the strap needs any other repairs. Now this extra thickness of metal at /will allow the surfaces s s., to be trued up or re-planed without touching the inner surfaces 1 1 2 . New brasses can then be fitted in the space A and the rod restored to good working order in a comparatively short time, and at a minimum cost. On the other hand, if there had not been any extra thickness of metal at / then as soon as the inner surfaces of the strap become worn, they will have to be re-planed from end to end, making the opening of the strap that is, the width from t to t. z too wide for the end of the rod ; and therefore, in this case, the strap will have to be heated and upset at k, so as to close the opening to fit the end of the rod. In doing so the holes i i will be thrown out of line, and otherwise cause considerable expense and an extra expenditure of time (which always means delay in getting the engine into service) before the rod can be brought into working order. The usual practice is to make the thickness of the strap at/J of an inch greater than at <j ; occasionally we find the difference between these thicknesses to be only -fa of an inch. When there is no key through the end k of the strap, the thickness at / is generally i of an inch greater than at //for small engines; and from g to * inch greater at A- than at// for large engines. When there is a key thnnigh the end k of 272 MODERN LOCOMOTIVE CONSTRUCTION. the strap, as shown in Fig. 417, the thickness of the metal at k is determined by the width of the key. In small engines, say engines with cylinders 14 inches in diameter, the thickness at k is generally such as to leave J inch metal at a (Fig. 417), that is, J inch metal at the outside of the wide end of the key. As the diameters of the cylin- ders are increased, the amount of metal at a is also increased at a rate which will give about 1 inch metal at a for engines with cylinders 20 inches in diameter. These dimensions here given are about the aver- age of those in common use. The width of the strap depends upon the length of the crank-pin journal, or the length of the crosshead pin. By deduct- ing from the lengths of these journals the thickness of the brass flanges, the width of the strap is at once determined. Hence in designing straps for locomotive main- or side-rods, about the only calculations which we have to make are those for finding the correct diameters and the number of bolts through the straps, and the correct thick- ness of the strap at g, Fig. 421. 301. Figs. 423, 424 represent another side-rod designed for a four-wheeled con- nected engine, such as is shown in Fig. 1 ; cylinders 17 x 24 inches. The whole de- sign of this rod differs from the designs of the rods previously shown. Straps are not used, but the keys are retained, so that the brasses can be adjusted. The rod itself is made thick and narrow at the ends; and thin and wide at the center. Figs. 425, 426, 427 represent the liner used between the keys and the brasses. The advantages claimed for this design will be considered hereafter MAIN-ROD BOLTS. 302. A bolt may be subjected to a sin- gle or a double shearing stress. Thus : Let A and B, Fig. 428, represent two plates which are connected by a bolt C. Now assume that a force is acting on the plate A in the direction of arrow 2 ; and another force acting on the plate B in the direc- tion of the arrow 3. In this case the bolt is subjected to a single shearing stress, LOCOMOTirK CONSTRUCTION. 273 because, it' tlic forces are great enough, the bolt will be severed in only one place, and the area through which the bolt will be severed is equal to the cross-sectional area of tin 1 bolt. In Fig. 429 the conditions are changed. Here we have a bolt connecting a rod and a strap. Assume now that a force is acting on A in the direction of the arrow 2, and another force acting on the strap in the direction of the arrow 3. In this case the bolt is subjected to a double shearing stress, because, if the forces are great enough, the bolt will be severed in two places, and the area through which the bolt will be severed will be equal to twice the cross-sectional area of the bolt. From this we infer that, if the diameter of the bolt in Fig. 428 is equal to the diameter of the bolt in Fig. 429, the force required to shear the bolt in the latter figure will be equal to twice the force required to shear the bolt in the former figure. Or, conversely, when the bolts in both figures-are subjected to the same shearing forces, the cross- it Fig. 428 Fig. 430 Fig. sectional area of the bolt in Fig. 428 must be equal to twice the cross-sectional area of the bolt in Fig. 429. From these considerations we learn that the area sheared is proportional to the shearing force to which the. bolt is subjected. 303. In determining the diameters and the number of bolts through the main-rod straps, we may assume, without impairing the results of our calculations, that these bolts are simply subjected to a double shearing stress. Here then the question arises : How great will be the shearing force to which the bolts through the main-rod straps are subjected? To this we answer : The shearing force to which the bolts are subjected will be equal to the maximum pressure on the main-rod. To find this maximum pressure we adopt the following graphical method : Fig. 430. Draw the straight line a b, and let it represent the center line of motion of the piston. On this line lay off any point a, and let this point represent the center of the driving axle. Through the point a draw the line c/ perpendicular to the line a b, and let the line c/represeut the vertical direction through which the axle box can move in the pedestal. On the line c/lay off a point rf; this point is to represent the center of the axle when the axle box touches the pedestal cap, consequently the distance between the points a and <l must be equal to the distance between the center line of motion a 6, and the lowest position that the center uf the axle can occupy in the pedestal. Again, on the line cf lay off a point <-; this point is to represent the center 274 MODERN LOCOMOTITE CONSTRUCTION. of the axle when the axle box touches the upper end of the pedestal, consequently the distance between the points a and e must be equal to the distance between the center line of motion a b and the highest position that the center of the axle can occupy in the pedestal. If now we find that the distance a d is greater than the distance a e, then from the point d lay off on the line c/a point c; the distance between the points d and c must be equal to one-half the stroke, or, in other words, equal to the length of the crank. If, on the other hand, the distance a e is greater than the distance a d, then from the point e lay off on the line c/a point/; the distance between the points e and / must be equal to one-half the stroke. But generally in locomotives, the distance a d will be found to be greater than a e, hence we shall confine our attention to that which happens below the center line of motion a I. From the point c as a center, and with a radius equal to the length of the connecting-rod, describe an arc cutting the line a b in the point I ; join the points c and b by a straight line, and thus completing the right-angled triangle a c I. Now the length of the side a b of this triangle will represent the total steam pressure on the piston ; the length of the side c b will represent the maximum pressure on the main-rod, and according to what has been stated before, the length of the side c b will also represent the shearing force to which the bolts in the rod are subjected. Therefore, as soon as we know the press- ure which the length of the side a b does represent, we will have no difficulty in determining the shearing force on the bolts ; because, as we have seen, the line a b I'epresents the total steam pressure, and this pressure is easily found by multiplying the area of the piston by the pressure per square inch ; the pressure on the main- rod due to the steam pressure will be as much greater than the total pressure on the piston, as the length of the line c b is greater than the length of the line a b, and consequently this pressiire can be found by a simple rule of proportion. In order to show plainly the manner of applying these principles, we will take the following example : EXAMPLE 84. It is required to find the shearing force to which the main-rod bolts are subjected in a locomotive whose cylinders are 16 inches diameter; stroke, 24 inches ; maximum steam pressure in the cylinders is 120 pounds per square inch ; length of the connecting-rod, 84 inches ; the distance (a d, Fig. 430) below the center line of motion of the piston through which the center of axle can move is 3 inches. In the first place, let us find the lengths of all the sides of a right-angled triangle, such as shown in Fig. 430, whose hypothenuse shall represent the pressure on the main-rod due to the steam pressure given in our example. The lengths of two sides of this triangle are already known, for we know that the side, or hypothenuse, c b must be equal to the length of the connecting-rod, namely, 84 inches. The length of the side a c must be equal to the sum of the distance a d, which is 3 inches, and one-half the stroke, which is 12 inches ; hence, the side a c will be 12 + 3 = 15 inches. The length of the side a b we must find by the well-known rule given in geometry for finding any side of a right-angled triangle when two of its sides are known. In the case before us we must subtract the square of the side a c from the square of the side c b, and extract the square root of the remainder. The square of the side b c is equal to 84 x 84 = 7056. MODERN LOCOMOTIVE CONSTRUCTION. 275 The square of the side a c is equal to 15 x 15 = 225. Subtracting the latter square from the former, we have 7056 225 = 6831. Extracting the square root of 6,831, we have \/6831 = 82.64 inches, which is the length of the side a b. The area of a piston 16 inches in diameter is equal to 201.06 square inches, and the total steam pressure on one piston will be equal to 201.06 x 120 = 24127.20 pounds. Hence line a b, which we have found to be 82.64 inches long, represents 24,127.20 pounds. The line c b we know to be 84 inches long, and since the pressure represented by the side c b will be as much greater than 24,127.20 pounds as c b is longer than a b, we have 84 x 24127.20 8264 - = 24524.25 pounds, which is the pressure represented by the line c b, and consequently is the press- ure on the main-rod, or the shearing force to which the bolts in the main-rod are subjected. 304. Our next step will be to find the area necessary to resist this shearing force, and this area will be equal to twice the total cross-sectional area of all the bolts through one end of the rod. In order to find this area we must first establish the stress which should be allowed per square inch, and this can best be established by finding the stress allowed by builders. For the sake of simplicity, we shall consider that the bolts are subjected to a shearing stress only, and shall consider that the total stress is equal to the total pressure on the main-rod. Now, assuming, as we have done before, that the pressure in the cylinders on locomotives at present in service, whose safety valves are set to 130 pounds, will be 120 pounds per square inch, and then determining by calculation the stress (due to the pressure of 120 pounds) which has been allowed per square inch of cross-sectional area of the main-rod bolts, we find that it varies in different locomotives from 7,000 to 9,000 pounds, and in one case we found it to be as high as 12,000 pounds per square inch. Our experience leads us to believe that, when the best quality of iron is used, 8,000 pounds per square inch of the cross-sectional area of the main-rod bolts will give good results, and should be adopted. The best quality of wrought-iron of which these bolts are generally made possesses an ultimate shearing strength of about 56,000 pounds per square inch ; if we now assume that these bolts are simply subjected to a shearing stress, and allow 8,000 pounds per square inch of section, we adopt 7 as a factor of safety. Hence, if the ultimate shear- ing strength of the iron is less than 56,000 pounds per square inch, say it is only 49,000 pounds, then the safe working stress to be allowed per square inch will be equal to 49000 = <000 pounds. From the foregoing remarks we conclude that twice the total cross-sectional area of the bolts that is, the area which has to resist the shearing force must be proper- 276 MODERN LOCOMOTIVE CONSTRUCTION. tioned so that the stress per square inch will be 8,000 pounds, provided the best quality of iron is used. After this, when the number and diameters of the bolts are to be established, we may be compelled to change this stress of 8,000 pounds per square inch, because the general practice in locomotive building is to avoid -fa and ^ of an inch in the diame- ters of the bolts, and therefore, in establishing the nearest number of bolts and adopting the nearest practical diameters to those for which the result of the calculations call, the stress may be somewhat greater or less than 8,000 pounds per square inch ; indeed, we may have to be satisfied as long as the stress falls within the limits of 7,500 to 8,500 per square inch for the best quality of iron. For an inferior quality of iron the stress should be less. Now, having established the stress to be allowed per square inch, we can easily find the total cross-sectional area of the main -rod bolts through one end of the rod by the following rule : RULE 54. Divide the total pressure on the main-rod, as found by the diagram, Fig. 430, by 8,000 ; the quotient will be twice the total cross-sectional area of the main- rod bolts through one of its ends. EXAMPLE 85. The total pressure on the main-rod given in Example 84 is 24,524.25 pounds ; what will be twice the total cross-sectional area of the bolts t 24524.25 = 3.065 square inches. 305. These bolts, as we have stated befoi*e, are tapered, hence when we speak of the diameters of the bolts we mean their small diameters. In a large number of locomotives the rear strap is wider than the front or crosshead strap. Careful observation seems to indicate that the diameter of any one of these bolts should be equal to about one-third the width of the rear strap ; in some engines the diameters are a little greater, and in others a little less, than this proportion. We may therefore assume that it is good practice to make the diameter of the bolt (as near as possible consistent with the avoidance of -fa or - 3 \ of an inch in the diameter) equal to one- third of the width of the rear strap. Hence we have the following rule : RULE 55. Divide the width of the rear strap in inches by 3 ; the quotient will be the diameter of the bolt. EXAMPLE 86. The width of the strap is 2f inches ; find the diameter of the bolts. which is nearly equal to ff inch. Avoiding -fa or -fa inch, we say the diameter of the bolts should be y- inch. Some builders will make these bolts | inch diameter. 306. When we know the diameters of the bolts, and also the total cross-sectional area which has to resist the shearing force, the number is easily determined by the following rule : RULE 56. Divide the total cross-sectional area of the bolts, as found by Rule 54, by twice the cross-sectional area of one bolt ; the quotient will be the number of bolts required. MODERN LOCOMOTIVE CONSTRUCTION. 277 EXAMPLE 87. The total cross-sectional area of the bolts subjected to shearing stivss is 3.065 square indies, the diameter of each bolt is if inch. How many bolts will be required I The cross-sectional area of a if -inch bolt is .69 square inch ; hence 3.065 = 2 ' 2 ' sa ? 2 bolts ' In this case the stress per inch, when the taper of the bolt is taken into account, which, for the sake of simplicity, has been left out of consideration, will not exceed 8,500 pounds. EXAMPLE 88. The total pressure on one main-rod of a locomotive cylinders 18 x 24 is 31,000 pounds ; the width of the strap is 2$ inches ; find the diameter and number of bolts. According to Rule 54, twice the total cross-sectional area of the bolts should be 31000 '= 3.87 square inches. According to Rule 55, the diameter of each bolt should be 75 -y- = .916, say f| inch. The cross-sectional area of a bolt if inch diameter is .69 square inch; hence, according to Rule 56, the number of bolts required will be 3 87 2~^-gg = 2 - 8 > sa y 3 bolts - Some locomotive builders use three bolts & inch in diameter for the same size of engine. EXAMPLE 89. The total pressure on one main-rod of a locomotive cylinders 20 x 24 is 38,000 poimds, strap 3 inches wide; find the diameter and number of bolts. According to Rule 54, the total cross-sectional area of the bolts will be 38000 8000 = 4.75. According to Rule 55, the diameter of the bolts will be 1 inch. The cross-sectional area of a bolt 1 inch in diameter is .7854; hence, according to Rule 56, the number of bolts through each end of i m od will be 4.75 2 x .7854 ~ There are engines of the same size running with only 2 bolts 1 inch in diameter through each end. We believe that 3 bolts, 1 inch diameter, for a maximum steam pressure of 120 pounds in a cylinder 20 inches diameter, will be safer and give better results. EXAMPLE 90. What should be the diameter of the bolt shown in the rear end of the main-rod, Figs. 431, 432! The cylinder is 12 x 16 inches; maximum steam pressure in the cylinder, 120 pounds; the distance through which the axle box can move below the center line of motion of the piston is 2 inches. 278 MODERN LOCOMOTirE CONSTRUCTION. Although the design of this rod is different from any we have previously shown, the foregoing rules are applicable. Here we will first have to find the total maximum pressure on the rod, as explained in Art. 303, and illustrated in diagram, Fig. 430. The area of a piston 12 inches in diameter is 113.1 square inches, hence the total pressure on the piston is equal to 113.1 x 120 = 13572 pounds ; consequently the line a b in our diagram, Fig. 430, represents 13,572 pounds. But the length of the line a I is not yet known, and must be found according to the instruc- tions given in Art. 303. In order to suit the conditions given in the example, the length of the line a c must be 10 inches that is, the sum of half the stroke (8 inches) and the distance (2 inches) through which the axle box can move below the center line of motion of the piston. The length of the line c b is equal to the length of the connecting-rod that is, the distance between the centers of journals and, as will be seen in Figs. 431, 432, this distance, or length of the connecting-rod, is 60 inches. Therefore the length of the line a I will be equal to V60 2 - 10* = 59.16 inches. Consequently, according to Art. 303, the line c b will represent 60 x 13572 ^ n 1g = 13^64./ pounds, oy.lb which is the maximum pressure on the main-rod. Twice the total cross-sectional area of the bolt to resist shearing must be, according to Rule 54. 13764.7 QAAA = 1.72 square inches, oUUU and 1.72 ^~ = .86 square inch, which will be the cross-sectional area of the bolt. The diameter of the bolt whose cross-sectional area is .86 square inch is nearly l-j^ inches, agreeing very closely with diameter of the bolt given in the illustration. 307. Figs. 431, 432 represent a main-rod, and Figs. 433, 434 a side-rod used on engines running on one of the elevated roads ; the cylinders of these engines are 12 inches diameter and 16 inches stroke. The rods are very good ones, and well adapted for these engines. The design of the main-rod differs from the designs of rods previ- ously given. Straps are not used; the rear end is an open one, which, after the bearings have been placed in position, is closed by the steel block A, firmly held in position by the bolt B. This bolt must be strong enough to resist the pull of the rod. The front end of the rod is designed to suit a class of crossheads with a single slide, such as is shown in Fig. 248. The design of the side-rod also differs from the designs of side-rods previously given. Here the straps have been retained, but keys are not used. MODERN LOCOMOTIVE CONSTRUCTION. 279 308. In the previous examples we have made the diameters of the maiii-rod bolts i -q i ml to oiie-third of the width of the rear strap as nearly as possible. The rear strap, as we have stated before, is generally made a little wider than the front one, so as to make the former stronger than the latter; the reason for this will be presently m rr> ----$ i^jTr <H_ i I -_^V-j,. TV Kt MM Fig. 433 - J^p =5*^=1 I ' 1 II & i I .- * nef-.~. <| Fig. 434 --XM i i 1 !j Searings of ^ 7F \-fhoiphor Bronze ,, '& \ Taper of Bolts X In 19 N~' I f J '' ^-4 j<f ix^ 1 M Steel 1 i sa . -331 _-_ 71 H~T / r. 432 i j,. jg* 1 explained. But, although the width of the rear strap differs from the width of the front one, the diameters of tin- bolts are nearly always m.-ulf Hie same for each ond. Again, iii the previous examples, the diameters of the bolts and their number 280 MODERN LOCOMOTIVE CONSTRUCTION. were made to suit a maximum steam pressure of 120 pounds per square inch of piston. The stress of 8,000 pounds per square inch of the cross-sectional area of the bolts was also established ; and since this stress should not be changed, no matter how great or small the maximum steam pressure in the cylinders may be, it follows that the rules previously given for determining the diameters and number of bolts through the main-rod are also applicable when the maximum steam pressure in the cylinder is greater or less than 120 pounds per square inch. When the steam pressure is greater than 120 pounds per square inch, then we shall generally require three bolts through each end of the main-rod for locomotives having cylinders 17 inches in diameter and upwards. Since the greatest number of bolts used through each strap is three (at least we have not met with cases in which this number was exceeded), the problems for solution may present themselves in the following form. EXAMPLE 91. Three bolts are to be used through one end of a main-rod for a locomotive having cylinders 18 x 24 inches. The length of the main-rod is 90 inches ; the maximum steam pressure in the cylinder is 160 pounds; the vertical distance below the center line of motion of the piston through which the center of axle can move is 3 inches. It is required to find the diameter of the bolts. In Art. 303 we have stated that the shearing force to which the bolts through one end of the main-rod are subjected is represented by the length of the hypothenuse c b of a right-angled triangle, Fig. 430, in which the length of the side a b represents the total steam pressure on the piston ; hence our first step, in the solution of our problem, will be to find the lengths of the sides of such a triangle. In Art. 303 we also have stated that the length of the hypothenuse must be equal to the length of the connect- ing-rod ; hence, in this case the length of the hypothenuse must be 90 inches. The length of the side a c, that is, the shortest side, must be equal to the sum of the length of the crank, and the vertical distance below the center line of motion through which the center of the axle can move ; hence, according to the conditions given in the example, the length of the side a c must be equal to 12 + 3 = 15 inches. The length of the side a b must be found by calculation as explained in Art. 303, thus : Eemembering that the length of the hypothenuse is 90 inches, and the length of the side a c is 15 inches, we have V90 2 - 15 2 = 88.74 inches, which is the length of the side a b. Now, having found the lengths of the sides of the right-angled triangle, we can easily determine the shearing force to which the bolts are subjected ; thus : The area of a piston 18 inches in diameter is 254.46 square inches ; therefore the total pressure on the piston at 160 pounds per square inch will be 254.46 x 160 = 40713.60 pounds. According to the remarks in Art. 303, the length of the side a b, namely, 88.74 inches, represents a pressure of 40713.60 pounds ; that is to say, the length of the side a b represents the total steam pressure on the piston. But we also know that the maximum pressure on the main-i*od is represented by the length of the hypothenuse of the same triangle, and that the maximum pressure on the main-rod is as much MODERN LOCOMOTIVE CONSTRUCTION. 281 greater as the length of the hypothenuse is greater than the length of the side a b. Hence we have 40713.60 x 90 Og^ - = 41291.68 pounds, which is the maximum pressiire on the main-rod; and this pressure also represents the total shearing force to which the three bolts are subjected. Since the stress per square inch is to be 8,000 pounds, twice the total cross- sectional area of the bolts that is, the whole area which has to resist the shearing force is found by Eule 54, and is equal to 41291.68 - = 5.16 square inches. o(JUU But our example requires that three bolts shall resist the shearing force, and since the bolts are subjected to a double shearing stress, twice the total area of the bolts which has to resist the shearing force will be equal to six times the cross-sectional area of one bolt ; hence we have 5 ' 16 Q p -~- = .86 square inch, which is the cross-sectional area of one bolt. The diameter of a circle whose area is .86 inch is nearly l^- inches; consequently the diameter of the bolts should be liV inches. 309. Figs. 435, 436 represent a main-rod, and Figs. 437, 438 represent a side-rod for a Mogul engine, that is to say, a locomotive having six driving wheels and a pony, or two-wheeled truck. In these engines the side-rods have to connect three pairs of driving wheels, and transmit motion to the front and rear pair. We have already seen that the design of the pedestal permits the driving axles to move up and down, so as to enable the driving wheels to adjust themselves to any unevenness of the track, consequently the centers of the axles will not always lie in a horizontal line. Under these conditions we cannot connect the three driving wheels on one side of the engine by a side-rod in which the crank-pin bearings are held rigidly in line. Consequently the side-rods in Mogul engines are made in two pieces, forming a front and rear side-rod for each side of the engine, as shown in Figs. 437, 438. The front and rear side-rods are connected by the pin S, which is placed at the back of the main-pin M. As far as the working of the engine is concerned, the pin 8 could be placed in front of the main-pin M ; but for the sake of convenience it is always best to place it at the back of the main crank-pin, so that it will at no time be covered by the main-rod, which, in nearly all Mogul engines, is placed outside of the side-rods. In fact, it often happens that, with the main-rods placed outside of the side-rods, the available space between the side- and main-rods will not be sufficient for the nuts on the pin S, and consequently this pin must be placed at the back of the main-pin M as shown. The pin S should also be placed as near as possible to the main crank-pin, so as to reduce the stress to which the strap around the main-pin is subjected to a minimum. 282 MODERN LOCOMOTIVE CONSTRUCTION. K- ,-,'Kio > v m r i ,f'i T*J* j, K-8 -^~* r " ^ %ot MODERX LOCOMOTIVE CONSTRUCTION. 1>S:; From the foregoing remarks we may conclude that in Mogul engines the front side-rods contain the bearings for the front crank-pin F and for the main crank-pin M; the rear side-rod simply contains the bearing for the rear crank-pin JR. MAIN-ROD STRAPS. 310. In Art. 300 we have stated that in designing the straps for locomotive main- ami side-rods, about the only calculations which we will have to make are those for finding the correct diameters for the bolts, number required, and the thickness of the strap represented by </, in Fig. 421. The rules for finding the number of bolts and their diameters have been given ; hence it now only remains for us to establish rules for finding the thickness of the strap at g. The weakest part of any locomotive main- or side-rod strap is in the plane x y or # 2 y., (Fig. 422), passed through the axis of the bolt. Consequently, when the width of the sti'ap is given, the thickness at <j must be determined by calculation so as to give a sufficient cross-sectional area in the plane x y to resist the forces acting on the strap. Of course, in the foregoing remarks we have assumed that the key has the best possible shape for the work it has to do (more of this hereafter), and that its thickness, as well as the diameter of the hole for the oil-cup, does not exceed the diameter of the bolts. The stress * in the main-rod straps is greater than that in the side-rod straps ; we shall, therefore, in this article, consider the strength of the main-rod straps only. Both the front and the rear straps are subjected to a tensile force that is, a force tending to tear the straps. But the centrifugal force to which the rear end of the rod is subjected brings into play on both straps a force which acts in a direction perpen- dicular to the length of the rod, or, in short, a transverse force ; this force acts with the greatest intensity at the back end of the rod, and becomes zero at the center of the crosshead pin. Yet there are portions of the front strap, which on account of their dis- tances from the center of the crosshead pin, are more or less subjected to a transverse force. Also, noticing that the bolts through the straps must necessarily be placed at some distance from the center of the pins, the transverse forces on both straps will act with a leverage, and therefore will act with a greater effect, and cause a greater stress in the straps, than they would do if the bolts could be closer to the center of the pins. Consequently, these latter forces must not be neglected in our calculations. But the transverse force acting on the rear strap is greater than the transverse force acting on the front one; and since the tensile forces are equal on both straps, it follows that the total stress in the rear strap is greater than the total stress in the front one. Again, the stress per square inch of cross-sectional area should be the same in both straps ; hence, it follows that, since the total stress is greater in the rear strap than that in the front one, the former should be made stronger than the latter, and this we often find to be the case in practice. But many master-mechanics prefer to " Stress" may be defined as the resistance to the alteration of form, and in this sense the word "stress" is here used. 284 MODERN LOCOMOTIVE CONSTRUCTION. make these straps of equal strength, for the following reason: The crosshead pin will wear in time to an oval form, making it smaller in the direction of the axis of the cylinder. If now the brasses in the front end of the rod do not touch each other, as is often the case, and the rod begins to pound, the key may be driven accidentally or carelessly too tight, causing the brasses to bind on the large part of the crosshead pin, throwing on the front strap an extra stress, which may, un- less the front strap is strong enough to resist this extra force, cause considerable damage. There is another fact which must not be lost sight of in proportioning a strap, namely, the bolt holes in the strap will in time wear to an oval shape, and then they must be re-reamed, thereby weakening the strap ; therefore it is necessary, in design- ing a strap, to make a slight allowance for re-reaming. Now, in order to determine accurately the thickness g of the strap, we should know the exact magnitudes of the forces to which they are subjected. But to find the exact magnitudes of these forces will be a difficult matter. Hence, taking all the given conditions into consideration, it will be an easier way, and probably the most practical one, to base our calculations on the proportions of straps used at present in locomo- tives running at high speeds, doing excellent service. We have seen that the weakest part of the strap is in the plane x y; hence, our first step will be to determine the cross-sectional area of the strap in this plane. Suppose, for the sake of simplicity, that the strap is subjected to a tensile force that is to say, a force acting in the direction of the length of the rod, or in a direction indicated by the arrow in Fig. 421 tending to pull the strap apart. In this strap we have two bolts, which we may assume resist aii equal amount of the pull, or, in other words, each bolt resists one-half of the pull. We therefore conclude that the metal of the strap in the plane x 2 y 2 has to resist one-half of the tensile force or pull to which the strap is subjected. But the force, acting on the metal in the plane x. 2 y- 2 , is transmitted to the plane x y, and this plane must also resist the tensile force trans- mitted to it by its own bolt. Therefore the metal of the strap in the plane x y must resist the whole tensile force to which the strap is subjected ; and the area of this metal must be proportioned accordingly. If we had three bolts through the strap, as is often the case, the conditions would not be changed that is to say, the weakest part of the strap, namely, its portion in the plane x y, must be made strong enough to resist the whole tensile force, and treated just the same as if no other portion of the strap had to resist any part of the force acting upon it. If, then, the straps are subjected to a tensile force pure and simple, as we have supposed, we can easily find the cross-sectional area at x y by allowing a stress of 10,000 pounds per square inch, as we have done, on the weakest part of a piston-rod, and consequently obtain the number of square inches in the cross-sectional area, by dividing the maximum pressure on the main-rod by 10,000 ; the quotient will be the required area through both wings y y., of the strap. But we have seen that these straps are subjected to forces acting in a direction perpendicular to the length of the rod, and these forces must not be neglected. But since it is difficult to determine the exact magnitude of these forces, we make allow- ances for them by reducing the stress per square inch due to the tensile force acting MODERN LOCOMOTIVE CONSTRUCTION. 285 oil these straps that is to say, we assume the straps to be subjected to a tensile force only, and reduce the stress of 10,000 pounds per square inch of cross-sectional area, so as to obtain a larger area. Hero, then, the question arises, How much stress per square inch shall we allow? For an answer to this question we must turn to the straps at present in use. In these straps we find that the stress per square inch of cross-sectional area in the plane x y varies, for the rear straps, from 6,000 to 7,000 pounds per square inch ; and when the front straps are made weaker than the rear ones, the stress per square inch for the former is in the neighborhood of 7,000 to 7,500 pounds per square inch. Our expe- rience leads us to believe that a stress of 6,500 pounds per square inch of cross- sectional area for rear strap, and a stress of 7,000 pounds per square inch for the front one, both made of the best quality of hammered iron, is good practice. These figures will be adopted in the following calculations. Hence we have the following rule : KULE 57. To find the thickness at g (Fig. 421) of the rear strap on the main-rod when the width of the same is given : Divide the maximum pressure on the main-rod by 6,500 ; the quotient will be the required number of square inches in the cross- sectional area at x y (Fig. 422). From the width of the strap subtract the diameter of the bolt ; the remainder will be the width of the metal at the weakest part of the strap. Divide the required cross-sectional area at x y by the width of metal at the weakest part of the strap ; one-half of this quotient will be the thickness of the strap at //. For finding the thickness of the front main-rod strap we use the same rule, with the exception that, instead of dividing the maximum pressure on the main-rod by 6,500, we divide it by 7,000. EXAMPLE 92. In a locomotive with cylinders 18 x 24 inches, and a maximum steam pressure in the cylinders of 120 pounds per square inch, we find by the method given in Art, 303 that the maximum pressure on the rod is 31,000 pounds; the width of the front and rear straps is 2f inches ; the diameter of each bolt through the straps is if inch ; it is required to find the thickness of the straps at g (Fig. 421). The total cross-sectional area at x y of the rear strap will be 31000 := *-76 square inches. The width of the metal at the weakest part of the strap that is, at x y will bo equal to 2? - if = llf = 1.8125 inches, and 4.76 L8125 = 2 ' 62 inches ' will be the sum of the thickness of both wings g g 2 of the strap. Therefore, 2.62 -^- = 1.31 inches, M say 1/g inches, is the thickness of the rear strap at g. 286 MODERN LOCOMOTIVE CONSTRUCTION, For the thickness of the front strap, we have 31000 700(7 = ^'^ S( l uare inches in the cross-sectional area at x y. and 2.43 4.42 _ 1.8125 ~ ' = 1.21 inches, say l-^- inches. NOTE. Some master-mechanics make the thickness of the front strap equal to that of the rear one ; therefore, in such cases, special calculations for the front strap will not be required. 311. Figs. 439, 440 represent two views of a main-rod for a consolidation engine that is, an engine with four pairs of drivers, and a pony truck, as shown in Fig. 4. ,_ j w_*r_ idf of thread The engine for which these rods were designed has cylinders 20 inches diameter and 24 inches stroke, and crossheads like that shown in Figs. 244, 246, and 247. For a high speed and a maximum steam pressure of 120 pounds in the cylinders, the rear strap on this rod is, in our opinion, too weak ; for the above given maximum pressure and for high speeds, safer and better results will be obtained by making the thickness of the strap around the bolts at least 1^ inches ; and also three }^ inch bolts should be used in place of two. SIDE-ROD STRAPS FOR EIGHT-WHEELED PASSENGER ENGINES. 312. In comparing the side-rod straps belonging to different locomotives of one and the same class and size, but designed in different locomotive establishments or by different master-mechanics, we find quite a variation in the dimensions of correspond- ing parts of the different side-rod straps around similar crank-pins. This is, no doubt, due to the fact that it is impossible to determine exactly the magnitude of the forces to which the side-rods are subjected. MODERX LOCOMOTirE CONSTRUCTION. 287 We have already seen that the main-rods are subjected to a tensile force, and also to a transverse force due to the centrifugal action at one of its ends. The side- rods are subjected to similar forces, but whose sum is of less magnitude than that of the forces acting on the main-rods. The magnitude of the tensile force acting on the main-rod is dependent on the whole pressure on the piston, whereas on side-rods the magnitude of the tensile force is dependent on the weight on the driving wheels, and partly also on the condition of the road-bed, and on the condition of the working parts under the engine; but the latter conditions will affect the tensile force acting on the side-rods to a greater degree than it will affect the tensile forces acting on the main-rods. If, for instance, the road-bed is not level, or the play between the axle box and the wedges has been increased by wear, or the engine is running over a sharp curve, the driving axles, as well as the side-rods, may at any time be thrown out of line with each other, thereby suddenly increasing the tensile force on the side-rods on one or the other side of the engine ; and when, under these conditions, the engine is running at a high rate of speed, this extra tensile force will act on the side-rods only, because these rods will be affected by the stored-up energy in the engine to turn the wheels, whereas the main-rods cannot be subjected to a greater pressure than that due to the pressure on the piston. Now, with these emer- gencies to provide for, it should not be a matter of surprise to hear of straps break- ing ; but the frequency of such occurrences can be avoided by basing our calculation on the designs of such straps which experience has taught us to be correct. In designing a side-rod strap we are guided by the same reasoning as that given in connection with the design of the main-rod straps, and therefore conclude that the weakest part of the side-rod strap is in the plane x y (Fig. 422) passed through the axis of the bolt. Since the width of the side-rod strap depends upon the dimensions of the crank-pin, we shall consider that the width has been given, and all that remains for us to determine is the thickness g (Fig. 421) of the wing of the strap. In eight-wheeled passenger engines two driving wheels are connected on each side of the engine; consequently, each main-rod in this class of engines has to t ransmit motion to two driving wheels ; and the side-rod has to transmit motion to only one driving wheel. The main driving wheels generally have to support a greater weight than the rear ones, as the former have to support a portion of the weight of the connecting-rods, a portion of the weight of the valve gear, and often have a heavier counterbalance than the latter ; but for the purpose of finding the proportions of the side-rod straps, we may assume that each driving whool, whether front or rear, supports an equal amount of weight. Again, the whole of the total steam pressure on the piston is not utilized for the purpose of giving motion to the driving wheels ; yet for the sake of simplicity we may assume that such is the case. Now, in order to simplify matters still more, we may again assume, as we did in relation to the main- rod, that the side-rods are subjected to a tensile force only. Consequently, since the main-rod in eight-wheeled passenger engines has to transmit motion to two driving wheels, and since the side-rod is, so to speak, only a connecting link between these two drivers, and therefore has only to transmit motion to one of them, it follows that, under tin- foregoing .assumptions, the tensile force to which the side-rods are subjected will be equal to one-half the pressure on the piston. Comparing the cross-sectional 288 MODERN LOCOMOTIVE CONSTRUCTION. area in the plane xy of the side-rod straps, at present working successfully, we find that the stress per square inch of the cross-sectional area in the plane x y, made by different makers, vai'ies, in round figures, from 3,500 to 4,700 pounds. Our experience leads us to believe that, for eight-wheeled passenger engines, it is good practice to make an allowance for a stress of 4,200 pounds per square inch of the ci'oss-sectional area through the weakest part of the strap (that is, in the plane x y), under the assump- tion that the side-rods are subjected to a tensile force only, and that the magnitude of this force is equal to one-half the steam pressure on the piston ; this stress of 4,200 pounds per square inch of the weakest part of the strap will be adopted in the follow- ing calculations. 313. In Art. 310 it will be seen that for main-rod straps the stress allowed per square inch in the plane x y is 6,500 pounds, but for the side-rod straps we have now established a stress of 4,200 pounds per square inch in a similar plane. This difference is due to the fact, as stated before, that side-rods are subjected to an additional tensile force when the engine is running over uneven road-beds, curves, etc. Therefore, in order to find the thickness at g of the side-rod strap (see Fig. 421), we divide the total steam pressure on the piston by 2 ; the quotient will be the assumed tensile force acting on the strap ; dividing this quotient by 4,200, we obtain the number of square inches in the smallest cross-sectional area of the strap that is to say, in the plane x y. Dividing this cross-sectional area by the width of the strap minus the diameter of the bolt, we obtain the sum of the thickness at g and </ 2 ; one-half of this sum will be the required thickness at g. This manner of finding the required thickness can be made simpler, hence the following : RULE 58. Divide the total steam pressure on the piston by 16,800 ; divide this quotient by the width of the strap from which the diameter of the bolt has been sub- tracted ; the last quotient will be the thickness at g of one of the wings of the side- rod strap. EXAMPLE 93. Find the thickness at g of the side-rod strap for an eight-wheeled passenger engine ; cylinders, 17 inches diameter ; maximum steam pressure on the piston, 120 pounds per square inch; width of strap, 24 inches; diameter of bolts through the straps, inch. The total pressure on the piston is equal to the product of its area in square inches into the steam pressure per square inch ; consequently the total pressure on the piston will be 226.98 x 120 - 27237.60 pounds. Dividing this pressure by 16,800, we have 27237.60 16800 = 1.621. Dividing this quotient by the width of the strap minus the diameter of the bolt, we obtain 1.621 ^~. 1 = 1.17+, say li inches, ^5 ~ 8 for thickness of the side-rod strap at g, Fig. 421. MODERN' LOCOMOTIVE 289 :;U. Iii Art. .'!09 wo have given the reasons for the use of two side-rods on each side of a Mogul engine. For similar reasons we need three side-rods on each side of a consolidation engine, namely, the front, central, and rear side-rods. h vi- dla. anttldt of tkread. t thread. 2*q U- t.-. i T | 33 v 4*r'H =' . _ e J 3 Jj T X <"<> outside of thrtad.' . 444 l\dla. outnlde of Ihread^fn t thread* \_\ ->_\ Figs. 441, 442 represent the front side-rod ; Figs. 44.'!, 444 represent the central side- rod ; and Figs. 445, 44ti represent the rear side-rod for a consolidation engine with cylin- ders 20 x 24 inches. It will be seen that the central side-rod connects two wheels ; the 290 MODERN LOCOMOTIVE COXSTHl'CTIOX. straps on this rod have forked ends, to which the front and rear side-rods are connected. This manner of connecting side-rods differs from the connection of the side-rods shown in Figs. 437, 438, in which the rear side-rod has the forked end, and r // % diam.outside of thread ,, . , * ~ Fig, 445 42-' . Vv Steel the strap around the main crank-pin is forged solid. Again, in the front and rear side-rods for the consolidation engine, provision has been made to take up the wear of the bearings in the ends of these rods which are connected to the central-rod. This makes a very good arrangement ; but it must not be understood that this design of side-rods is always adopted in consolidation engines, and that the design of side-rods shown in Figs. 437, 438 is only suitable for Mogul engines. There are many consoli- dation engines in which the side-rods are connected in a manner precisely similar to that of connecting the side-rods in Mogul engines. 315. In nearly all eight-wheeled passenger engines, 4 feet 8.J inches gauge, the side-rods are placed outside of the main-rods, and therefore the brass bearings, straps, etc., at each end of the side-rod will be equal in size. In some of the narrow-gauge engines we sometimes find the side-rods plased inside of the main-rods. In such cases the brass bearing at one end of the side-rod will be larger than that at the other end of the same rod. Locomotive builders sometimes make the straps for such rods of equal thicknesses. We believe that in such cases the better practice will be to find the thickness of the strap at the small end of the rod by Rule 58, and then increase the thickness of the strap at the large end of the side-rod ten per cent., provided the widths of the straps are equal, which is generally the case. SIDE-BOD STRAPS FOR MOGUL ENGINES. 316. In Mogul engines the stress in the side-rods will as in eight-wheeled pas- senger engines depend on the weight on drivers, the condition of the road-bed, and the condition of the engine, as we have explained in connection with side-rods for passenger engines. But in Mogul engines we have two other elements not found in passenger engines which are detrimental to the strength of the side-rod strap, namely, UODERX LOCOMOTITE CONSTRUCTION. 291 Fly. ~Kigi<l-Wheel Sate XOQUZ a larger number of driving wheels, and the knuckle joint that is, the connection of the two side-rods as shown at S in Fig. 438. 317. Fig. 447 represents the wheel base of a Mogul engine ; the main- and side- rods are indicated simply by their center lines. In this class of engines the main pair of driving wheels B is placed between the front pair A and the rear pair C, but is not placed centrally between them. The rigid wheel base will often depend on the length of the boiler ; and the distance between the wheels will in many cases depend on the general design of the boiler and the valve gear. Although these driving wheels are not placed at equal distances apart, tin- arrangement of the equal- izing levers is such as to throw as nearly as possible the same amount of weight on each driver. For the purpose of designing the side-rod straps, we may assume that an equal amount of weight is placed on each driver. In order to simplify the rule for finding the thickness of the strap, we shall again assume, as we did in the case of passenger engines, that the whole steam pressure on the piston is utilized for the purpose of giving motion to the wheels. Now, since three drivers are connected on each side of the engine, and since the same amount of weight is assumed to be placed on each driver, it follows that one-third of the total steam pressure on one piston will, according to our assumption, be required to turn one driving wheel. When the driving wheels are turning in the direction as indicated by the arrows, and the crank-pins are below the centers of the axles, the front side-rod D will be subjected, besides the transverse forces acting upon the rods, to a tensile force ; and the rear side-rod K will be subjected to a compressive force, each equal to one-third of the pi'essure on the piston, provided the engine is running over a straight and perfect level road. On the other hand, when the crank-pins are above the center of axle, the front side-rod will be subjected, besides the transverse forces acting upon the rods, to a compressive force and the rear side-rod to a tensile force, each again equal to one-third of the pressure on the piston. The exact magnitude of the transverse forces acting on the side-rods under the various conditions of the road-bed, etc., cannot be determined, but the total steam pressure on the piston is known ; we therefore assume, as in the case of passenger engines, that the side-rods are simply subjected to a tensile force due to the pressure on the piston ; design the straps accordingly, and make allowances for the other forces, as will be hereafter explained. If now we had no transverse forces acting on the straps to contend with, we would simply divide one-third of the maximum piston pressure by 10,000 pounds (which is about a fair allowance for stress per square inch when we have to provide against a simple tensile force), and thereby obtain the number of square inches in the cross-sectional area through the weakest part of the strap. But since we have to provide against the transverse forces, we must divide one-third of the maximum steam pressure on the piston by a number less than 10,000, and shall adopt, as before, 4,200. Hence, if we divide one-third of the maximum steam pressure on the 292 MODERN LOCOMOTIVE COXSTRVCTIOX. piston by 4,200, we shall obtain the number of square inches in the cross-sectional area through the weakest part of the strap. Dividing this area by the width of the strap minus the diameter of the bolts through it, and again dividing the quotient thus obtained by 2, we obtain a thickness for the side-rod straps which we shall indicate by the letter A. But this thickness A will not be sufficiently great, for the following reasons : In adopting the number 4,200, or, in other words, allowing one square inch for every 4,200 pounds of the pressure on the strap due to one-third of the maximum piston pressure, we provide for the transverse forces acting on the strap, and also for the extra tensile forces due to the condition of the road-bed and condition of the engine, such as will occur in passenger engines. This extra tensile force, due to the condition of the road-bed, etc., will be greater in Mogul engines, on account of the increased number of wheels, than in passenger engines ; and besides this we have the knuckle joint to contend with. We therefore add to the thickness A previously found, -nf of an inch for the rear and front strap, and add f of an inch for the central strap, for all Mogul locomotives having cylinders 13 inches diameter and upwards. For Mogul engines having cylinders whose diameters are less than 13 inches, add ^ of an inch to the thickness A for the front and rear straps, and --fa of an inch to the thick- ness for the central strap. These rules can be stated in a simpler manner, as follows : RULE 59. To find the thickness g (Fig. 421) for the side-rod straps around the front and rear crank pins in Mogul engines having cylinders 13 inches diameter and upwards : Divide the total maximum steam pressure on one piston by 25,200 ; divide the quotient thus obtained by the width of the strap from which the diameter of the bolts through it has been deducted, and add -f- 6 - of an inch to the last quotient ; the sum will be the required thickness. For Mogul engines having cylinders less than 13 inches in diameter, divide the total maximum steam pressure on the piston by 25,200; divide the quotient thus obtained by the width of the strap from which the diameter of the bolts through it has been deducted, and add J of an inch to the last quotient ; the sum will be the required thickness g for the side-rod strap around the front and rear crank-pin. RULE GO. To find the thickness g for the side-rod strap around the main crank- pin in Mogul engines having cylinders 13 inches diameter and upwards : Divide the total maximum steam pressure on the piston by 25,200; divide the quotient thus obtained by the width of the strap from which the diameter of the bolts through it has been deducted, and add % of an inch to the last quotient ; the sum will be the required thickness. For Mogul engines having cylinders less than 13 inches diameter, divide the total maximum steam pressure on the piston by 25,200 ; divide the quotient thus obtained by the width of the strap from which the diameter of the bolts through it has been deducted, and add -fa of an inch to the last quotient ; the sum will be the thickness g for the central side-rod strap. EXAMPLE 94. Find the thickness y (Fig. 421) for the side-rod straps for a Mogul engine whose cylinders are 18 inches diameter; maximum steam pressure on the piston, 120 pounds per square inch ; width of front and rear straps, 2j inches ; diame- ters of the bolts through these straps, if inch ; width of central strap, 2J inches ; diameters of bolts through the same, lr- 6 - inches. MODERX LOCOMOTIfK CONSTRUCTION. 293 Let us first find the thickness for the front and rear straps. The total maximum steam pressure on the piston is found by multiplying the area of the piston in square inches by the steam pressure per square inch; hence we have 254.47 x 120 = 30536.40 pounds. 30536.40 25200 Subtracting the diameter of a side-rod bolt from the width of the strap, we obtain 2.25 - .9375 = 1.3125 inches, and 1.211 10 7 = .922, say |f of an inch, which is the thickness A, to which -n,- inch must be added. Hence jjf + ^y = l inches, which is the thickness g of the front and rear side-rod straps. To find the thickness g of the central side-rod strap, we divide, as before, the total maximum steam pressure on the piston by 25,200, and obtain 1.211. This quotient \ve divide by width of the central strap minus the diameter of the bolt. We have 1.211 2.5 - 106 = ' say ^ an mc ' which is the thickness A. To this we must add g of an inch ; the sum J + | = li inches, which is the thickness g of the central side-rod strap. EXAMPLE 95. What should be the thickness of the side-rod straps for a Mogul engine whose cylinders are 11 inches diameter ; rear and front straps, If inches wide ; bolts, inch diameter ; central side-rod strap, 2 inches wide ; bolts, f inch diameter ; maximum steam pressure on the piston, 120 pounds per square inch? Total maximum steam pressure on the piston will be equal to 95.03 x 120 = 11403.60 pounds, and 11403.60 252CO To find the thickness g for the front and rear strap, we have first .452 divided by the width of the straps minus the diameter of the bolts, equal to .452 1.75 - .75" == 4:> -' say * inch ' which is the thickness A. To this we must, according to rule, add \ of an inch. We therefore obtain i + J = f inch for the thickness g for the front and rear side-rod straps. For the thickness g of the central side-rod straps we have 1 1403.60 2.VJOO = ' 4>)2 ' and .452 -_> _ 7;, = -361, say 3 inch, 294 MODERN LOCOMOTIVE CONSTRUCTION. which is the thickness A. To this we must add -fa inch. Therefore t + i 7 ^ = H inch, which is the thickness y for the central side-rod strap. 318. For all Mogul engines in which the maximum steam pressure on the piston is 120 pounds per square inch, we believe it is good practice not to make the thickness ff of any side-rod strap less than 2 of an inch. If our calculations, according to the foregoing rules, call for a thickness less than inch, then the results indicate that the width of the strap is excessive, and it should be reduced. SIDE-ROD STRAPS FOR CONSOLIDATION ENGINES. 319. Fig. 448 represents the wheel base for a consolidation engine. Here we have four wheels connected on each side of the engine. The wheel marked A is one of the first pair of drivers, B one of the second pair, C one of the third pair, and I) one of Fiff. &4S b ^ Total TT/teel Sa.se COlf fO LID A.TU)Jf ENGINE Fig. 450 the rear or fourth pair of drivers. In some engines of this class the main-rods are connected to the second pair of drjvers. The front side-rod E, the central side-rod F, and the rear side-rod r, and also the main-rod M, are represented by their center lines only. MODERN LOCOMOTIVE CONSTRUCTION. 295 Iii tliis class of engines the equalizing levers are arranged, as in the former class, to throw, as nearly as possible, an equal amount of weight on each driver; hence for the purpose of designing the side-rod straps we may again assume that all drivers have in l)i>ar an equal amount of weight; we may also assume, as in the former cases, that tlu> whole steam pressure on the piston is utilized for rotating the wheels. Since four wheels are connected on each side of the engine, it will require, under the forego- ing assumptions, one-fourth of the total steam pressure on the piston to turn each wheel. When the wheels are connected, as shown in Fig. 448, the front side-rod E will have to transmit motion to one wheel ; that is, the wheel A ; the central side-rod F will have to transmit motion to the second wheel B, and by a little reflection it will be seen that the same side-rod F has also to transmit motion, through the front rod E, to the fi-ont wheel A. We may therefore say that the work performed by the central side-rod /<' is equal to twice that performed by the front rod E, and conclude that under our assumptions the tensile force acting on the side-rod F, due to the steam pressure on the piston, is equal to one-half of the total maximum pressure on the piston ; and that the tensile force acting on the front side-rod E is eqtial to one-fourth of the total maximum steam pressure on the piston. Such conclusion will be correct so long as the engine is in first-class condition, and running over a perfect and straight road. But when the engine is running over curves, and the road-bed is not perfect, and the wear has caused play between the axle boxes and the wedges, the ratio between the tensile forces acting on the central and front side-rod will not be exactly as two to one. Again, since the action at one end of the contra! side-rod is equal to the reaction at the other end, we conclude that the straps on this rod should be of equal dimen- sions. Furthermore, practice has shown that the stress on the front and rear side-rods is somewhat less than that on the central rod. The thickness g (Fig. 449) of the side-rod straps, obtained by the following rules, will agree with modern practice. RULE 61. To find the thickness at g (Fig. 449) for the front and rear side-rod straps, for consolidation engines : Divide the total maximum steam pressure on the piston by 3l3,(iO(); divide the quotient thus obtained by the width of the strap minus the diameter of the bolts through it ; add fa of an inch to the last quotient ; the sum will be the required thickness. KULE 62. For finding the thickness of the central side-rod straps, divide the total maximum steam pressure on the piston by 33,600; divide this quotient by the width of the strap, minus the diameter of the bolts through it, and add jj of an inch to the last quotient ; the sum will be the required thickness at // (Fig. 449). EXAMPLE 96. What should be the thickness of the side-rod straps for a consoli- dation engine having cylinders '20 indies diameter? Maximum steam pressure on the piston, 1_() pounds. The width of the central side-rod straps, and also the width of the front and rear side-rod straps, is 2i inches; the diameter of the bolts through the central side-rod is 1| inches; the diameter of the bolts through the front and rear straps is 1 inch. 296 MODERN LOCOMOTIVE CONSTBVCT10N. The area of a piston 20 inches in diameter is 314.16 square inches. The total maximum steam pressure 011 the piston will be 314.16 x 120 = 37699.20 pounds, and 37699.20 33600 The thickness at fj for the front and rear side-rod straps will be equal to 1.122 tvTirT + -fa =- lie inches, very nearly. The thickness for the central side-rod straps will be 1.122 2> _ -j, + S = 1*6 inches, very nearly. 320. After the thickness at g (Fig. 449) for the side-rod straps has been obtained, we determine the thickness at /and & in a manner similar to that adopted for finding these thicknesses for the main-rod straps namely, the thickness at/ is made of an inch greater than at g, and the thickness at k is made J of an inch thicker than at g for small engines, and from f to inch greater for large engines. In some straps we find the hole o for the oil-cup drilled through the whole thick- ness of the wing ; in others, we find this hole drilled only part way through the wing, and then a smaller hole s about of an inch in diameter drilled through the remain- ing part of the thickness, as shown in Fig. 449. The latter we believe to be the best practice, as this will not reduce the strength of the strap as much as when the large hole is drilled clear through. SIDE-ROD BOLTS. 321. In considering the strength of the bolts which fasten the straps to the main-rods, we have seen (Art. 303) that the principal force to which these bolts are subjected is a shearing force. In determining the number and diameter of these bolts we made their cross-sectional area proportional to this force, with certain allowances for the other forces to which they are subjected. It was further seen (Art. 308) that for the light main-rods two bolts through each strap are sufficient for the work they have to do ; but that for the heavy class of main-rods three bolts through each strap must be used, so as to obtain the required cross-sectional area, and at the same time avoid the use of bolts of excessively large diameters ; or, we may say, bolts whose diameters are out of proportion to other parts of the rod. But now, in considering the strength of bolts required to hold the straps to side-rods, it may be stated, at once, that more than two bolts through each side-rod strap are not required, because two bolts will always give us a sufficient cross-sectional area without using bolts of excessively large diameters. Even in the heaviest loco- motives which up to the present time have been built, it has been found that two bolts through the side-rod straps are sufficient to resist all the forces to which they are LOCOMOTIVE CONSTRUCTION. 297 subjected, and yet the diameters of these bolts did not appear to be too large, or, in other words, the bolts did not require so much metal to be drilled out of the straps as to increase the thickness of the wings of the straps to an unreasonable extent. Of course, for practical reasons which are obvious, less than two bolts through each end of the side-rod cannot be used. Therefore we may say that the number of bolts through each side-rod strap (namely, two), for any locomotive, is established. In order to find the diameter of bolts for side-rod straps, we should know the exact mag- nitudes of the forces to which they are subjected; but to determine the magnitude of these forces accurately is impossible ; in fact, the same remarks made in relation to forces to which the side-rod straps are subjected are also applicable to the forces which tend to break the bolts through the straps. We must therefore again allow experience to guide us in forming the following rules: For all practical purposes we may proceed in our calculations for finding the diameters of the side-rod strap bolts as if these bolts were subjected to a simple shearing force only, due to the weight on the driving wheels. Therefore, in the following calculations we shall simply find, first, the diameter of the bolts required to resist a shearing force, and then add to this diameter a certain amount to allow for the forces due to the unevenness of tracks, loose boxes, etc., which sum will also be sufficient for the stress due to the momentum of the rod. 322. Let us first consider the diameters of bolts required for side-rod straps in eight-wheeled passenger engines. We have already seen that, in this class of engines, there are two driving wheels on each side, and that the motion to the rear driving wheel is transmitted through the side-rod, which connects the two. Now let us assume, as we have done before, that the whole steam pressure on the piston is utilized in giving motion to the wheels. Under this assumption, the force acting in the direction of the length of the side-rod will be equal to one-half the total maximum steam pressure on the piston, and will represent an assumed shearing force, to which the bolts are subjected. Now, having established, for the purpose of our calculations, a shearing foi'ce, we next determine an area proportional to this force, and this may be done in a manner similar to that adopted for finding cross-sectional area of the main-rod strap bolts, namely, divide the pressure on the side-rod, which in this case is assumed to be equal to one-half of the total maximum steam pressure on the piston, by 8,000; the quotient will give us an area proportional to our assumed shearing force; but since this area is greater than that required for the actual shearing force, we have also made, to a great extent, an allowance for the force due to the momentum. For the sake of brevity, hereafter we shall refer to this area as a simple shearing area, and the force to which it is proportioned the shearing force. Having found the required shearing area, the cross-sectional area of one bolt is readily found. Since in all side- rod straps two bolts are used, and since the shearing force tends to cut each bolt in two places, it follows thai the shearing area must be equal to four times the cross- sectional area of one bolt; hence we divide the former area by 4; the quotient will be the cross-sectional area in inches of one bolt ; the diameter corresponding to the last area will be the diameter of the bolt required to resist the shearing force. In order to allow for the forces due to uneven tracks, etc., we must add of an inch to the diame- 298 MODERN LOCOMOTIVE CONSTRUCTION. ter thus found ; the sum will be the required diameter of the side-rod bolts in eight- wheeled passenger engines. This rule can be stated in a simpler manner, as we shall presently show. In Mogul and ten-wheeled engines we have three driving wheels connected on each side of the engines ; we therefore divide one-third of the maximum steam pressure on the piston by 8,000 ; the quotient will be the shearing area in square inches ; dividing this area by 4, we again obtain the cross-sectional area of one bolt, the diameter of which must also be increased by some given amount to resist the additional forces which come into play. This additional amount will be given in the rules which are to follow. The diameters of the bolts through side-rod straps in consolidation engines are found in a manner similar to the foregoing. In these engines we have four wheels, connected on each side, consequently we divide one-fourth of the maximum steam pressure on the piston by 8,000, so as to obtain the shearing area of the bolts through the front and rear straps ; dividing the latter by 4, we obtain the cross-sectional area of one bolt, whose corresponding diameter must again be increased by a certain amount, as will be given in the following rules : RULE 63. To find the diameter of a side-rod strap bolt for an eight- wheeled pas- senger engine : Divide the total maximum steam pressure on the piston by G4,000 ; the quotient, will be the cross-sectional area of one bolt required to resist the sheai'ing force. To the corresponding diameter of this area add ^ of an inch ; the sum will be the required diameter of the bolts. EXAMPLE 97. The diameter of the cylinders of an eight-wheeled passenger engine (such as is shown in Fig. 1) is 18 inches ; maximum steam pressure per square inch of piston, 120 pounds ; find the diameter of the side-rod bolts. The total maximum steam pressure on the piston is equal to its area multiplied by 120. The area of an 18-inch piston is equal to 254.47 square inches ; and 254.47 x 120 = 30536.4 pounds. 30536.4 64000 =0.4/7 square inch. The nearest diameter of a bolt corresponding to a cross-sectional area of 0.477 square inch is || inch; neglecting the ^ of an inch and adding of an inch to the diameter found, we have f + = J inch, which is the required diameter of the side-rod strap bolts for eight-wheeled passenger engines. RULE 64. To find the diameters for the side-rod strap bolts in a Mogul engine : Divide the total maximum steam pressure on the piston by 96,000 ; the quotient will be the cross-sectional area in square inches of one bolt necessary to resist the shearing force. To the corresponding diameter, which we designate by the letter A, add of an inch ; the sum will be the required diameter of the bolts through the straps around the front and i % ear crank-pin. Again, to the diameter A add f of an inch ; the sum will be the required diameter of the bolts through the straps around the central or main crank-pin. EXAMPLE 98. Find the diameters for the side-rod bolts in a Mogul engine, having cylinders 19 inches in diameter ; maximum steam pressure per square inch of piston, MODEBX LOCOMOTIVE CO\STJIUCT1(>.\. 299 120 pounds. The area of a 19-inch piston is 283.53 square inches; the total maximum pressure on the piston will be equal to 283.53 x 120 = 34,023.6 pounds. 34023.6 ,, . = 0.3o4 square inch. The nearest diameter corresponding to an area of 0.354 square inch is $- inch. Therefore 1 + i = H inch, which is the diameter for the bolts through side- rod straps for the front and rear crank-pin. And }$ + I = IMJ inch, which is the diameter of the bolts through the side-rod strap for the central or main crank-pin. RULE 65. To find the diameters for the side-rod strap bolts in a consolidation engine: Divide the total maximum steam pressure on the piston by 128,000; the ijuotient will be the cross-sectional area in square inches of each bolt through the front and rear straps necessary to resist the shearing force. To the corresponding diameter, which we shall designate by the letter B, add of an inch ; the sum will be the required diameter of the bolts through the straps for the front and rear crank- pins. Again, to the diameter B, add inch; the sum will be the diameter of the bolts through the straps for the second and third crank-pins. EXAMPLE 99. Find the diameters for the side-rod bolts in a consolidation engine having cylinders 20 inches in diameter ; maximum steam pressure per square inch of piston, 120 pounds. The area of a 20-inch piston is equal to 314.16 square inches ; the total maximum steam pressure on the piston will be equal to 314.16 x 120 = 37699.2 pounds. 37699.2 1^8000 " square inch. The nearest diameter corresponding to an area of 0.294 square inch is inch. Therefore f + f = 1 inch, which is the diameter of the bolts through the straps around the front and rear crank-pins. And + = l inches, which is the diameter of the bolts through the straps for the second and third crank-pins. 323. The bolts through the side-rod and also through the main-rod straps should be placed as close to the keys as possible, leaving only sufficient room to tighten the nuts. The distance rf, Fig. 449 or Fig. 451, that is, the distance from end of the wing of the strap to the first bolt, is generally made equal to about one and a half times the diameter of the bolt. The distance from center to center of bolts varies from 2 to 3 inches, depending on the diameters of the bolts ; for engines with cylinders 16 inches in diameter and upwards, this distance is generally 3 inches, and for engines having cylinders 10 or 11 inches, it is _' indies, and in some cases even less than that. Good practice seems to indicate that these bolts should be as close to each other as a sufficient clearance for the wrench will allow. The side-rod bolts are generally tapered, the taper varying from ^ to of an inch in 12 inches. The diameters of the bolts found in the foregoing calculations are the small diameters. 324. The cross-section of the keys is usually rectangular. We believe the better practice will be to round off the side H, as shown in Figs. 449, 450, because it has been found that, when keys of rectangular cross-section are used, the strap is 300 MODERN LOCOMOTIVE CONSTRUCTION. liable to crack, as indicated at p in Fig. 450, which shows that sharp corners at these points impair the strength of the strap. The thickness of the key is generally made from to \ of an inch less than the diameters of the bolts. The width a at the small end of the key (Figs. 449, 451) varies from one to one and a half times the diameter of the bolts ; the latter is preferable for main-rods, the former for side-rods. The length / of the key is usually made equal to one and a half times the total width of the strap. The taper of these keys varies from f to Ij inches in 12 inches ; the former is the most common. Although sometimes the keys are made of wrought-iron, the best practice is to make them of steel. 325. Figs. 451, 452 represent a main-rod whose front end is designed to connect to a crosshead working between two slides, similar to the one shown in Figs. 241, 243. 1 -*'- i tat -* -v-s The key in the front end is inserted horizontally, because there is not sufficient room between the projecting ends of the crosshead to place the key vertically. The key is necessarily made short, so as to clear other parts of the machinery. It bears against a cast-iron block (7, which, when the key is drawn in, forces the brasses B B 2 against each other. The bolt D simply prevents the cast-iron block from slipping out of position. MODERN LOCOUOTirE CONSTRUCTION. 301 FORMS OF BODS. 326. The favorite locomotive main-rod is the solid one of rectangular form that is to say, a rod whoso tranverse section is similar to that shown in Fig. 453 ; they are made stiff enough so as not to buckle. Main-rods are subjected alternately to a tensile and compressive force, due to the steam pressure on the piston; the intensity of these forces is increased by the obliquity of the rods, and also by positions of some of the mechanism which at times must work out of alignment when the engine is running over curves or uneven tracks. The compressive force has a tendency to buckle the rods in the direction of arrow 2 (Fig. 457) ; in order to prevent buck- ling in this direction, a definite thick- ness at C and D (Fig. 457) will bo required ; in all main-rods this thick- ness is uniform throughout. The main-rods are also subjected to a transverse force, due to the centrip- etal acceleration, and this force has a tendency to bend or break the rod in the direction of arrow 3 (Fig. 456) ; to prevent any change of form in this direction, a definite depth at A and B will be required ; this depth increases uniformly from A to B. The thickness and depth of main-rods, made by different builders and master- mechanics, for the same class and size of locomotives, vary somewhat, but the average of good practice seems to point to the following proportions : In the smallest transverse section of a main-rod, that is, at A, the depth / h, Fig. 453, should be equal to If times the thickness fg ; the depth at B, Fig. 456, should be 25 per cent, greater than that at A ; and furthermore, the area of the trans- verse section at A should be such as to contain 1 square inch for every 5,000 pounds Fig. 453 fill. 454 Fig. 455 I Fig. 450 Fig. 457 of the total maximum steam pressure on the piston. Hence, within the limits of ordinary locomotive practice, we may adopt the following rules, which arc based upon the proportions just given. RULE 66. To find the area of the smallest transverse section of a main-rod, that is, the area of the cross-section at A, Fig. 45(i, divide the total maximum steam press- 302 MODERN LOCOMOTIVE CONSTRUCTION. ure on the piston by 5,000 ; the quotient will be the number of square inches in the area of the transverse section at A. EXAMPLE 100. The maximum steam pressure on the piston of a consolidation engine is 120 pounds per square inch, cylinders 20 inches diameter ; what should be the number of square inches in transverse section through the smallest part of the main-rod! The area of a 20-inch piston is 314.16 inches ; the maximum steam pressure on the piston will be equal to 314.16 x 120 = 37699.20 pounds, and the number of square inches required in the area of the smallest cross-section of the main-rod will be equal to 37699.20 rnnn ' Si square inches. RULE 67. To find the thickness and depth of the main-rod at its smallest transverse section, that is, at A, Fig. 456, and also the depth of the rod at B, multiply the cross- sectional area of the smallest section of the rod, as found by Eule 66, by 4, and divide the product by 7 ; the square root of the quotient will be the required thickness C or D (Fig. 457) in inches. To find the depth of the rod at A, multiply the thickness of the rod in inches by 1.75 ; the product will be the depth in inches at A. For the depth at B, increase the depth of A by 25 per cent. EXAMPLE 101. What should be the thickness and depth of a main-rod for a consolidation engine having cylinders 20 inches diameter, steam pressure on piston 120 pounds per square inch ? Here we must first find the area in square inches of the smallest cross-section of the rod, that is, at A. In the last example we found this area to be 7.53 inches. Hence, the thickness of the rod will be equal to 7.53 X 4 nv i - = 2.07 inches. 7 The depth of the rod at A will be equal to 2.07 x 1.75 = 3.62 inches. The depth at B will be equal to 3.62 x 1.25 = 4.52 inches. Avoiding fractions less than ^ inch, we find that the thickness of this rod should be 2 1 1 6 inches; the depth at A, 3jj inches; and the depth at B, 4^ inches. EXAMPLE 102. What should be the thickness and depth of a main-rod for an eight-wheeled passenger engine having cylinders 18 inches diameter, maximum steam pressure in cylinder 140 pounds per square inch ? The total maximum steam pressure on the piston is equal to 254.47 x 140 = 35625.8 pounds. According to Eule 66, the area of the smallest cross-section should be equal to 35625.8 ~~k7vvr~ = '-12+ square inches ; and according to Eule 67, the thickness of the main-rod will be equal to 7.12x4 XODERX LOCOMOTIVE CONSTRUCTION. 303 The depth of the rod at A will be equal to 2.02 x 1.75 = 3.53 inches. The depth of the rod at B will be equal to 3.53 x 1.25 = 4.41 inches. Avoiding fractious less than ^ inch, the thickness of the rod will be 2 inches ; depth at A, 3J inches; and depth at B, 4,^ inches. It will be noticed in these examples that in the small tranverse section of the rod tin 1 side /A, Fig. 453, is If longer than the side f <j. Should it be required to have a different ratio between these sides, say that / h shall be If longer than / <?, then multiply the area in square inches, as found by Rule 66, by 8, and divide the product by 13 ; the square root of the quotient will be the thickness ; and the thickness thus found multiplied by If, or 1.625, will give the depth of the rod at A. The foregoing rules are applicable to locomotive main-rods only; and even in locomotive practice, these rules will give satisfactory results only so long as the length of the main-rod is not greater or much greater than 60 times the width of the rod found by these rules. Main-rods whose lengths are greater than 60 times the thick- ness, or connecting-rods for other engines in which this ratio and the maximum steam pressure on the piston differs greatly from ordinary locomotive practice, should be treated as upright columns or pillars, with rounded or pointed ends supporting a load ; and the dimensions of these rods should be found by rules given in books treating on the strength of materials. Sometimes we find locomotive main-rods with the edges chamfered, whose cross- sections will appear as shown in Fig. 454. This we believe to be bad practice, as it ruts the metal away in places where it is needed the most. Chamfered edges do not add to the beauty of a rod, but unnecessarily increase the expense of making them, and when done no advantage whatever is gained. The best practice is simply to take off the sharp corners to as small degree as possible, so as to prevent a person cutting liis hands or otherwise hurting himself in oiling, cleaning, or inspecting a locomotive. Sections of rods, as shown in Fig. 455, should also be avoided, because such forms only impair the strength of the rod without gaining any advantage. 327. Main-rods are often made of iron, sometimes of steel ; when of the former, the bt-st quality of hammered iron must be used. The rules for finding the dimensions of main-rods (given in Art. 326) are suitable for rods made of the best hammered iron. When made of steel they may be made slightly lighter. But since, in many cases, steel rods are adopted simply for the purpose of ensuring greater safety, and not so much for the purpose of reducing the weight, no difference in the dimensions between iron and steel rods is made. For the sake of convenience in designing, we have given the following tables containing the dimensions for iron main-rods. These have been determined by the rules given in Art. 326. In the dimensions given we have avoided those containing less than one -j^ of an inch, and selected such as agreed nearest with the decimals found. 304 MODERN LOCOMOTIVE CONSTRUCTION. TABLE 22. THICKNESS AND DEPTH OF MAIN-RODS AT THE SMALL AND LARGE ENDS. RODS MADE OF BEST HAMMERED IRON. MAXIMUM STEAM PRESSURE PER SQUARE INCH OF PISTON, 120 POUNDS. Diameter of Cylinders. Thickness. Depth at Small End. Depth at Large End. 9" H" If" 2" 10" i" 1-ft" 2*" 11" H" 2" 24" 12" 13" H" if" 2A" 2|" 2f" aft" 14" 15" 16" iV ift" 14" 2ft" 2J" 2J" 3,%" 3|" 3f" 17" if" V 31" 18" u 3J" W 19" 2" W' 4" 20" 2ft" 3|" 44" 21" 2,V 3||" 4f" 22" 2ft" 4" 5" TABLE 23. THICKNESS AND DEPTH OF MAIN-RODS AT THE SMALL AND LARGE ENDS. RODS MADE OF BEST HAMMERED IRON. MAXIMUM STEAM PRESSURE PER SQUARE INCH OF PISTON, 130 POUNDS. Diameter of Cylinders. Thickness. Depth at Small End. Depth at Large End. 9" 1" Itt" 2i" 10" U" ir 2|" 11" 1ft" aA" 2ft" 12" 1ft" 2i" 2[f" 13" 1ft" 2|" 3,V 14" 14" 2J" 3" 15" If" 2jg" 3i" 16" 1J" 3" 3i" 17" iff" 3ft" 4" 18" iH" 3f" 4i" 19" *S" 3ft" 4i" 20" 24" 3f" 4H" 21" 2" 3}g" 4^|" 22" 2f" 4*" 5ft" TABLE 24. THICKNESS AND DEPTH OF MAIN-RODS AT THE SMALL AND LARGE ENDS. RODS MADE OF BEST HAMMERED IRON. MAXIMUM STEAM PRESSURE PER SQUARE INCH OF PISTON, 140 POUNDS. Diameter of Cylinders. Thickness. Depth at Small End. Depth at Large End. 9" 1" It" 2ft" 10" H" iff" 2ft" 11" i" 2*" 2H" 12" ift" 2f" 2W 13" i,y 2ft" 3ft" 14" i ;" 2f" 3ft" 15" 1M" 211" 3-fI" 16" I" 3i" 3H" 17" lit" 3ft" 4i" 18" 2" 3i" 4|" 19" 2i" 3H" 4" 20" 24-" 3^" 4|" 21" 2f" 4i" 54" 22" 21%" 4ft" 5|" \ioi>j-:i;.\- COSSTRVCTION. 305 TABLE 25. THICKNESS AND DEPTH OF MAIN-BODS AT THE SMALL AND LARGE ENDS. RODS MADE OF BEST HAMMERED IRON. MAXIMUM STEAM PRESSURE PER SQUARE INCH OF PISTON, 150 POUNDS Diameter of Cylinders. Thickness. Depth at Small End. Depth at Large End. 9" iiV' US" 2i" 10" H" 2" 2J" 11" U" " 2f" 12" If" 2A" 3" 13" H" 2" 3J" 14" 14" art" 31" 15" It" 3" 3f" 16" if" 3i" 4" 17" W" 3,V 4" 18" -',',," 31" *ft" 19" 2ft" 8J" 4i 1" 20" 2ft" 4ft" 5ft" 21" 2, 7 6 " 4i" 5 A,-" 22" -',",," 4ft" 5ft" TABLE 26. THICKNESS AND DEPTH OF MAIN-RODS AT THE SMALL AND LARGE ENDS. RODS MADE OF BEST HAMMERED IRON. MAXIMUM STEAM PRESSURE PER SQUARE INCH OF PISTON, 100 POUNDS. Diameter of Cylinders. Thickness. Depth at Small End. Depth at Large End. 9" It's" 11" 2ft" 10" 1ft" 2ft" 2f" 11" 1ft" 2ft" 2?" 12" 13" 1ft" i,y 84" 2ti" 3i" 3f" 14" Hi" 2ir 3J" 15" Hi" 3i" air 16" MS" 3ft" 4ft" 17" 2ft" 3ft" 4,'," 18" 2ft" 3f" 4J" 19" 2ft" 3 It" *" 20" 2f" 4ft" 5i" 21" 21" 4|" 5i" 22" 2i" 4$" 51" SIDE-KODS. 328. When we consider all the conditions under which a side-rod must transmit motion from one wheel to another, it will be seen that to design such a rod is not as easy as to design a main-rod. We have seen that a main-rod should be stiff enough to do its work without buckling in any direction ; and since we can estimate very closely the pressure to which it will be subjected, its strength to resist these pressures can be readily determined, as shown by the foregoing rules. Side-rods, however, labor under disadvantages to which the main-rods are not subjected. Wear will create play between the axle boxes and wedges, allowing the axles to run out of their proper adjustment, thereby throwing an extra stress on the side-rods ; uneven tracks will throw the side-rods out of parallelism, which will again increase the stress on the rods ; unequal wear of tires, which practically means a difference in the diameter of the 306 MODERN LOCOMOTIVE CONSTRUCTION. wheels, and consequently that one or the other wheel must slip a certain amount during each revolution; but this slip, due to the unequal diameters of the wheels, cannot take place through any other agency than the side-rod, and consequently the rod will again be subjected to an extra thrust or pull. But slip is not only due to the unequal wear of tires ; it is also caused by the form of the tread of tires, and, as we have seen in previous articles, many tires have a cone tread ; consequently, in curving, the wheels having such treads will run on one side of the engine on larger diameters than on the other side, and consequently slip must occur. Another feature which presents itself in connection with curving is that the play between the axle boxes and wedges will cause the axles to run out of parallelism, and all this tends to throw extra stress on the side-rods. Comparatively sudden stopping by the application of brakes, running over slippery places on the rails, or incautious use of sand often plays mischief with the side-rods. Now, these conditions are the disadvantages under which a side-rod labors, and may at times throw on it extraordinary pressures which cannot be accurately deter- mined, but can only be appi'oximately estimated. Side-rods should be made as light as possible, so as to reduce the stresses due to the action of the centrifugal force to a minimum, yet they must be strong enough to resist the tensile and compressive forces to which they are alternately subjected. When side-rods are subjected to a compressive force or thrust, they must not buckle in a vertical direction, that is, in the direction of arrow 2, Fig. 458 ; yet, under certain circumstances, it is desirable that they should, to a limited extent, slightly spring or buckle in a horizontal direction, that is, in the direction of arrow 3. The reason for desiring a slight spring of the side-rods in a horizontal direction is to obtain a certain I Fig. 458 i Ifi *' Fig. 459 amount of flexibility, so as to avoid excessive jerks on the rod and crank-pin, and thereby lessen the danger of heating the crank-pin brasses, or breaking the crank-pins or side-rods. Here we notice a difference between the essential conditions demanded from a main-rod and a side-rod ; the former must do its work without buckling in any direction, the latter should not buckle in a vertical direction, but should have a certain amount of flexibility by springing to a slight extent in a horizontal direction ; and these requirements the designer should not lose sight of. Now, a side-rod which shall meet all the demands made upon it must have a proper distribution of metal, and must also be of such a form as will reduce the cost of manufacture to a minimum. Consequently, various types of side-rods are now in use. In the early stages of locomotive building, many side-rods with circular transverse sections were used, the diameter of the central section being larger than the diameters M(>l>i:i;\ LOCOMOTIl'K fOXSTRVCTION. 307 of the end sections. This type of rod was finally abandoned, because, although cheap to manufacture, it had the same rigidity vertically and laterally, which, as we have seen, is objectionable. Probably the most popular type of side-rod at present in use is that shown in Figs. 458, 459. This rod has a uniform, rectangular tranverse section throughout. It 1ms a certain amount of flexibility in the direction of arrow 3, and is, comparatively, not a costly rod to make. This rod is extensively used both for freight and passenger engines. On account of its cheapness, it is nearly always adopted for freight engines ; I Fig. 46O \\ 1 | <r ' ; fig. 461 Fig. 462 Fig. 463 but for fast passenger service its metal is not considered to be correctly distributed, and, consequently, we now frequently meet with passenger engines for which a type of side-rod such as is shown in Figs. 460, 461 has been adopted. The transverse section of this rod is of the I form, as shown in Fig. 464, drawn to a larger scale than Figs. 460, 461. For some rods the section is made uniform throughout ; in others, it is deeper at the center than at the ends. The advantage of this form of rod is that, with an amount of metal equal to that used for a rod with a solid rectangular section, its depth can be made greater than the depth of the latter, and consequently it is stronger to resist the action of the centrif u- ' gal force. On the other hand, the opinion prevails among a num- ber of master-mechanics that this rod does not possess the required flexibility sideways, and we believe that, on this account, it is not generally adopted. A difference is also made by different designers in the distribution of metal throughout the transverse section ; the proportions given in Fig. 464 we find sometimes adopted, whereas, for the same class and size of engines, we occasionally find the proportions of the cross-section to be like those shown in Fig. 419. The type of side-rod shown in Figs. 462, 463 has been used on some railroads for a number of years, and is said to bo one of the best type of rods in use. As will be seen, it is made deeper at the center than at the ends, but its thickness at the center is Fig. 464 308 MODERN LOCOMOTIVE CONSTRUCTION. less than at the ends. In it are combined the best features of the rods shown in Figs. 458 and 4GO. On account of its increased depth at the center, it is stronger to resist the action of the centrifugal force than the rod shown in Fig. 458 ; and on account of its decreased thickness at the center, it has a greater flexibility than the one shown in Fig. 460. But it is an expensive rod to make, and therefore we believe it is not as often adopted as its merits deserve. PROPORTIONS OF SIDE-RODS. 329. In Art. 328 it was seen that there are many causes which at any time may increase the stress on a side-rod, and may increase it to such an extent as will cause fracture of or injury to the rod. The total stress to which the side-rods may at any time be subjected can only be determined by experience and close obser- vation of the behavior of the side-rods in every-day service, and facts obtained in this way will enable us to establish rules for guidance in designing other side-rods for similar locomotives. The following rules are empirical, and will hold true only within the limits of ordinary locomotive practice. In eight-wheeled passenger engines, the side-rods are longer than those used in consolidation engines ; and since the length of the rods has an important bearing upon the size of the cross-section, that is to say, for longer rods we require a greater cross- section, it follows that the side-rods for consolidation engines have generally a smaller cross-section than that of the rods for passenger engines, diameter of cylinders and maximum steam pressure being the same in both cases. Again, in consolidation engines the front and rear side-rods have less work to do than the central side-rod, and therefore the cross-section of the latter rod is generally made greater than that of the front and rear rods. In Mogul and ten-wheeled engines, the length of the rear side-rods is generally equal to the length of the side-rods in passenger engines of the same power ; but the front side-rods in the former classes of engines are generally shorter, and therefore the cross-sectional area of the front rods is often made less than that of the rear side- rods. Yet this is not a universal practice, as in these classes of engines we meet with many in which all the side-rods are of equal cross-section. Similar remarks apply to consolidation engines ; that is to say, in a number of engines of this class, there is no difference made' in the cross-sectional area of the side-rods, whereas in others the cross-sectional areas for the front and rear side-rods are made less than that of the central rods. Here, then, we see that practice differs, and therefore in establishing our rules we shall follow the average of good practice. 330. In comparing the side- and main-rods made by different builders, we find that the cross-sectional area of the side-rods is generally about ten per cent, less than the cross-section at the smallest part of the main-rod. Consequently, to find the cross- section of side-rods for passenger engines, we have the following rule : RULE 68. Divide the total maximum steam pressure on the piston by 5,500 ; the quotient will be the number of square inches in the cross-sectional area of the side- rod for eight-wheeled passenger engines. .MIH:I;\ LOCOMOTIVE CONSTRUCTION. 309 Kx AMPLE 103. In a passenger engine having cylinders 18 inches in diameter, the maximum steam pressure on the piston is 140 pounds per square inch; what should he the cross-sectional area of the side-rod? The maximum steam pressure on the piston is 254.47 x 140 = 35625.8 pounds, 35625 8 and ' - = 6.47 square inches in the cross-sectional area of the side-rod. In practice a difference exists between the ratio of the thickness to depth of the side-rods, but observation indicates that two and a half times the thickness for the depth is a good proportion ; and this we shall adopt for side-rods in passenger engines. Hence we have the following rule: RULE 69. To find the thickness and depth of side-rods for passenger engines : Multiply the cross-sectional area of the side-rod (as found by Rule 68) by 2, and divide the product by 5 ; the square root of this quotient will be the thickness. Multiply this thickness by 2 ; the product will be the depth of the side-rod. EXAMPLE 104. Find the thickness and depth for a side-rod for an eight-wheeled passenger engine with cylinder 17 inches diameter ; maximum steam pressure on the piston, 150 pounds per square inch. The maximum steam pressure on the piston is 226.98 x 150 = 34,047 pounds. According to Rule 68, the cross-sectional area of the side-rod should be 34047 _. , ,r = 6.19 square inches. According to Rule 69, the thickness of the side-rod should be (tin V V - = 1.57 inches = 1-ft inches nearly. 5 And the depth should be 1.57 x 2.5 = 3.92 inches = 31f inches nearly. Hence the side-rod should be 1 & inches thick, and 3 jf inches deep. The foregoing rules will only hold true for side-rods made of the best quality of hammered iron, whose lengths for cylinders 9", 10", and 11" in diameter do not exceed 6 feet 6 inches ; for 12", 13", 14" cylinders, 7 feet 6 inches ; for 15", 16", 17" cylinders, 8 feet 6 inches; and for cylinders 18 inches diameter and upwards, 9 feet. For shorter rods in this class of engines, the cross-sectional area could be somewhat reduced; but for the sake of uniformity of templates, etc., such close adjustment of the cross-sectional area to the length of the side-rod is not usually observed. The appended tables have been arranged by the foregoing rules. 331. From what has been said in the beginning of the foregoing article, it will be seen that the dimensions of the side-roils given in the following tables can be used for the rear side-rods in Mogul, and also for the rear side-rods in ten-wheeled engines. And since the front side-rods in these classes of engines are shorter than the rear ones, we believe it to be good practice to reduce the cross-sectional area of the front roils. In nearly all Mogul and ten-wheeled engines, the thickness of the roar side-rods is equal to the thickness of the front ones; consequently, when we wish to reduce the cross-sectional 310 MODERN LOCOMOTIVE CONSTRUCTION. area of the front rods, we have only to reduce their depth, according to the following rule. EULE 70. To find the depth for the front side-rod : Multiply the depth of the rear side-rod (taken from the following tables) by .08 ; and subtract the product from the depth of the rear side-rod ; the remainder will be the depth of the front rod. EXAMPLE 105. What should be the dimensions of the cross-section for a front side-rod in a Mogul engine, having cylinders 18 inches diameter, maximum steam pressure on the piston 140 pounds per square inch? Looking in Table 29, we find that for a cylinder 18 inches diameter, the rear side- rod should be If inches thick, and 4 inches deep. Since the thickness of the rods is not changed, we know that the thickness of the front side-rod should be If inches. According to Rule 70, the depth of the front rod should be equal to 4 inches - (4 x .08) = 3.68, say 3f inches. TABLE 27. THICKNESS AND DEPTH OP SIDE-RODS OP UNIFORM RECTANGULAR CROSS-SECTION, MADE OP THE BEST HAMMERED IRON, FOR EIGHT-WHEELED PASSENGER ENGINES. MAXIMUM STEAM PRESSURE ON THE PISTON, 120 POUNDS PER SQUARE INCH. Diameter of Cylinders. Thickness. Depth. 9" i" 11" 10" Jr; 2ft" 11" 2J" 12" i" 2ft" 13" ift" -'! i 1 ," 14" ift" 21" 15" H" 34" 16" ift;; 3ft" 17" 3i" 18" 14" 3fi" 19" ift" W' 20" if 44" 21" ir 4ft" 22" ifl" 4i" TABLE 28. THICKNESS AND DEPTH OP SIDE-RODS OF UNIFORM RECTANGULAR CROSS-SECTION, MADE OP THE BEST HAMMERED IRON, FOR EIGHT-WHEELED PASSENGER ENGINES. MAXIMUM STEAM PRESSURE ON THE PISTON, 130 POUNDS PER SQUARE INCH. Diameter of Cylinders. Thickness. Depth. 9" H" itt" 10" 4" 2i" 11" " 2f" 12" i" 2ft" 13" H" 2f" 14" 1ft" 3" 15" U" 3ft" 16" if" 3ft" 17" W 3|" 18" ift" 31" 19" it" 4ft" 20" if 4ft" 21" Hi" *r 22" If' 4f" MODERy LOCOXOTirE COSSTRVCTION. 311 TABLE 29. THICKNESS AXD DEPTH OF SIDE-RODS OP UNIFORM RECTANGULAR CROSS-SECTION, MADE OF THE HEST HAMMKRED IRON, FOR EIGHT-WHEELED PASSENGER ENGINES. MAXIMUM STEAM PRESSURE ON THE PISTON, 140 POUNDS PER SQUARE INCH. Diameter of Cylinders. Thickness. Depth. 9" W 2" 10" 1" 2ft" 11" +4" 2ft" 12" 1ft" 2|" 13" H" 2J" 14" U" 3ft" 15" 1ft" 3ft" 16" 17" 1ft" H" 3ft" 3f" 18" 19" 20" 21" 22" It" Itt" If li" 2" 4" 4J" i TABLE 30. THICKNESS AND DEPTH OF SIDE-RODS OF UNIFORM RECTANGULAR CROSS-SECTION, MADE OF THE BEST HAMMERED IRON, FOR EIGHT-WHEELED PASSENGER ENGINES. MAXIMUM STEAM PRESSURE ON THE PISTON, 150 POUNDS PER SQUARE INCH. Diameter of Cylinder-. Thickness. Depth. 9" 48" 2ft" 10" 1 ft// 16 2ft" 11" 12" u;; 2t" 13" 3" 14" ift" 3i" 15" U" Q 7 // 16" u ",, 3li" 17" 3)f" 18" it" 44" 19" 20" 21" 22" it" V 2" 1" TABLE 31. THICKNESS AND DEPTH OF SIDE-RODS OF UNIFORM RECTANGULAR CROSS-SECTION, MADE OF THE UKST HA.M.MKKED IRON", FOR EIGHT-WHEELED PASSENGER ENGINES. 5IAXIMUSI STEAM PRESSURE ON THE PISTON, 160 POUNDS PER SQUARE INCH. Diameter of Cylinders. Thickness. Depth. 9" 10" ft" 2f" 11" ift" 24" 12" H" 2|" 13' if 3ft; 14" 1h.ii Te 15" ! ', 16" ir 3{'' 17" it" 4ft' 18" 19" JB// 1 1 a// 4ft' 20" j 1ft'/ 4t" 21" 2" V 22" 2ft" 312 MODERN LOCOMOTIVE CONSTRUCTION. 332. In finding the dimensions for the side-rods for consolidation engines, the best mode of procedure will be to find first the dimensions for the central one. We have already seen that these rods are shorter than those in passenger engines, and therefore the cross-sectional area of the central side-rods for consolidation engines is generally less than that of the side-rods for passenger engines. Observation indicates that the average of good practice is to give one square inch in the cross-sectional area for every 6,000 pounds of the maximum steam pressure on the piston ; and that the depth of the central side-rod is about 2 times its thickness. Hence we have the following rules : RULE 71. To find the cross-sectional area of the central side-rods for consolida- tion engines : Divide the total maximum steam pressure on the piston by 6,000 ; the quotient will be the number of square inches in the cross-sectional area. EULE 72. To find the thickness and depth of the central side-rods for consolida- tion engines : Multiply the cross-sectional area (found by Eule 71) by 2, and divide the product by 5 ; the square root of this product will be the thickness. Multiply this thickness by 2j ; the product will be the depth. EXAMPLE 106. What should be the thickness and depth of a central side-rod for a consolidation engine having cylinders 20 inches diameter ; maximum steam pressure on the piston, 140 pounds per square inch I The maximum steam pressure on the piston is 314.16 x 140 = 43982.4 pounds. According to Eule 71, the cross-sectional area should be 43982.4 = 7-33 square inches. And according to Eule 72, the thickness should be 7.33 x 2 ., ,.-, . T - = 1.71 inches. 5 The depth should be 1.71 x 2.5 = 4.275 inches. Avoiding thirty-seconds of an inch, we find that the thickness should be If inches, and the depth, 4J inches. The front and rear side-rods in consolidation engines have less work to do than the central ones, hence the cross-sectional area of the former can be less than that of the latter. In nearly all consolidation engines the thickness of all the side-rods remains the same ; we have therefore only to find the depth of the front and rear rods, which can at once be obtained by deducting a certain amount from the depth of the central one ; the remainder will be the required depth for the front and rear side-rods. EULE 73. To find the depth of the front and rear side-rods for consolidation engines : Multiply the depth of the central side-rod by .08, and subtract the product from the depth of the central one ; the remainder will be the depth of the front and rear side-rods. EXAMPLE 107. What should be the thickness and depth of all the side-rods for a consolidation engine, having cylinders 22 inches diameter ; maximum steam pressure on the piston, 140 pounds? We first find the dimensions of the central rod. The total maximum steam pressure on the piston is 380.13 x 140 = 53218.2 pounds. MODERN LOCOMOTIVE CONSTRUCTION. 313 According to Rule 71, the cross-sectional area of this rod should be 53218.2 liINN) = 8.86 square inches. According to Rule 72, the thickness of all the side-rods should be 5.86 x 2 = 1.88 inches. The depth of the central side-rod should be 1.88 x 2.5 = 4.70 inches. And the depth of the front and rear side-rods should be 4.70 - (4.70 x .08) = 4.33 inches. Avoiding thirty-seconds of an inch, we find that the thickness of all the side-rods should be 1$ inches ; the depth of the central one should be 4|J inches ; and that of the front and rear rods, 4| inches. The appended tables have been computed by the foregoing rules. TABLE 32. THICKNESS AND DEPTH OP SIDE-RODS OP UNIFORM RECTANGULAR CROSS-SECTION, MADE OP THE BEST HAMMERED IRON, FOR CONSOLIDATION ENGINES. MAXIMUM STEAM PRESSURE ON THE PISTON, 120 POUNDS PER SQUARE INCH. Diameter of Cylinders. Thickness of all the Side- rode. Depth of Central Side- rod. Depth of Front and Rear Side-rode. 14" 1ft" 2f" 21" 15" i,V 3" 2f" 16" 1*" 34" 2J" 17" 1ft* 3|" 3iV' 18" w' 3ft" si* 19" 11" 3f" 3ft" 20" 1ft" :!!;: 3|" 21" it!" 44" 3{|" 22" it" 4f" 4" TABLE 33. THICKNESS AND DEPTH OP SIDE-RODS OP UNIFORM RECTANGULAR CROSS-SECTION, MADE OP THE BEST HAMMERKI) IKON, FOR CONSOLIDATION KM JINKS. MAXIMUM STEAM I'KKSSURE ON THE PISTON, 130 POUNDS PER SQUARE INCH. Diameter of Cylinder*. Thickncm of all the Slde- rods. Mc'jith of Central Side- rod. Depth of Front and Rear Side-rods. 14" 15" If li- 24" v 2|" 2(2" 16" lt" 3t" 3ft" 17" i,V 31" 3i" 18" 11" 3" 3" 19" l,v 3J" W' 20" 11" 4ft" 3t" 21" 22" Ifr 4t" 41" 4" 41" 314 MODERN LOCOMOTIVE CONSTRUCTION. TABLE 34. THICKNESS AND DEPTH OP SIDE-RODS OP UNIFORM RECTANGULAR CROSS-SECTION, MADE OP THE BEST HAMMERED IRON, FOR CONSOLIDATION ENGINES. MAXIMUM STEAM PRESSURE ON THE PISTON, 140 POUNDS PER SQUARE INCH. Diameter of Cylinders'. Thickness of all the Side- rode. Depth of Central Side- rod. Depth of Front and Rear Side-rods. 14" 1ft" 3" 2f" 15" Ii" 3ft" 2ir 16" If" 3,V 3*" 17" iV 3|" 3f" 18" H" 31" 3i" 19" 20" If 1 It" 4ft" 4i" 3J" M" 21" 22" 1" if if 4H" 44" 4|" TABLE 35. THICKNESS AND DEPTH OF SIDE-RODS OF UNIFORM RECTANGULAR CROSS-SECTION, MADE OF THE BEST HAMMERED IRON, FOR CONSOLIDATION ENGINES. MAXIMUM STEAM PRESSURE ON THE PISTON, 150 POUNDS PER SQUARE INCH. Diameter of Cylinders. Thickness of all the Side- rods, Depth of Central Side- rod. Depth of Front and Rear Side-rods. 14" 15" 14" ift" 3ft" 8ft" ati" 3ft" 16" W' 31" 3i" 17" ii" 3t" 3ft" 18" l*" 4" 3|" 19" itt" 4ft" 3|" 20" H" 4ft" 4ft" 21" if" 4|" & 22" ill" 41" 4ft" TABLE 36. THICKNESS AND DEPTH OF SIDE-RODS OF UNIFORM RECTANGULAR CROSS-SECTION, MADE OF THE BEST HAMMERED IRON, FOR CONSOLIDATION ENGINES. MAXIMUM STEAM PRESSURE ON THE PISTON, ICO POUNDS PER SQUARE INCH. Diameter of Cylinders. Thickness of all the Side- rods. Depth of Central Side- rod. Depth of Front and Rear Side-rods. 14" Ii" 3ft" art" 15" If" 3ft" 34" 16" 1ft" 3|" 3f" 17" 1ft" 31" 3ft" 18" If 4i" 3f" 19" If" 4ft" 4" 20" ill" 4ft" 4ft" 21" l" 4||" 4,y 22" 2" 5" 4f" MODEItX LOCOMOTIVE CONSTRUCTION. 315 ROD BRASSES. 333. All main- and side-rods for which straps are used are provided with brass boxes, generally called " brasses." These are made in pairs, one brass being an exact duplicate of the other. All main-rod brasses for the crank-pin should be babbitted. We have known a few instances in which no Babbitt metal was used, but such, as far as we have seen, proved to be a failure. Even when these boxes were made of phosphor bronze, Babbitt metal was required to keep them cool. Figs. 465, 466 represent the brasses in a main-rod for the crank-pin, and show the rr "I i i * ' i! y I j F.n,.46 5 L -' 1TTT JLU H -S H Fig. "466 i J amount and the location of the Babbitt metal a a 2 a. 2 in these brasses. Sometimes these strips of Babbitt metal are made of uniform width throughout, but we believe the best practice is to make the ends nar- rower than the central parts, as shown in Fig. 466, which will prevent the babbitt from slipping out of position. In many cases these strips are placed at equal distances apart, as shown in Fig. 465, but we believe the best practice is to increase the distances between the strips jind the joint of the brasses, so as to bring the center of the strips on lines drawn from the center of the hole to the corners of the brasses, or nearly so. With this ar- rangement the strips will be in those portions of the brasses which contain the greatest amount of metal, and will not be so detrimental to the strength of the brasses as in the positions shown. Fig. 467- Fig. 468 316 MODERN LOCOMOTIVE CONSTRUCTION. Side-rod brasses should also be babbitted, but there are many in use without it. When Babbitt metal is used, it is inserted either as shown in Figs. 465, 466, or as shown in Figs. 467, 468. The former method we believe to be the best one, because, with the Babbitt metal extending clear across the brasses, the crank-pin will wear more evenly than with the Babbitt metal inserted as shown in Figs. 467, 468. This latter method should never be adopted for the crank-pin brasses in main-rods. 334. In many locomotives the side-rod brasses are made similar in form to that shown in Figs. 467, 468, and in a few instances they are made similar to that shown in i'j i fon i 1 H^j *"*rf*l --,f u .Fty. 470 i i *f .i I UL.JJ i inJ I j L h---, I L - ! TT I Lf4<J JF%. 4<*9 '-<U-<U 1 W-J Figs. 469, 470. The difference between these two forms is, that one set is provided with caps e, as shown in Fig. 470, which are cast to the brasses ; tho other set is made up of plain brasses that is to say, they have no caps. These caps cover the end of the crank-pin ; their purpose is to keep the crank-pin, as much as possible, free from dust. The caps answer the purpose for which they have been designed ; but they are detrimental to the examination of the condition of the pin which they cover ; and consequently they are not as frequently adopted as the ordinary plain brasses. In Fig. 465 it will be noticed that the flanges of the brasses do not extend to the edges of the strap ; there are many main-rods as well as side-rods which have brasses of this design. But there is an objection against the flanges stopping short of the edges of the strap. The brasses are exposed to considerable dust, and as soon as they become a little loose, the dust will work in between the flanges and strap, and wear ridges in the latter, so that, when it becomes necessary to replace the brasses, the straps must be re-planed before the new brasses can be used. Re-planing straps should be avoided as much as possible, as it reduces their strength; consequently we must prevent, as much as possible, unequal wear and the formation of ridges in the sides of the straps. This desired result is obtained, to some extent, by allowing the MODERN LOCOMOTITE CONSTRUCTION. 317 flanges of the brasses to cover the whole width i (Fig. 469) of the strap, and also cover the solid end of the same. Since one brass is a duplicate of the other one, the depth of the flange at C appears to be and is excessive ; yet, on account of the practical advantages gained by making the flanges so deep, there are, probably, at present more brasses with deep flanges used than brasses with flanges stopping short of edges of the strap. 335. The thickness I (Fig. 469) of the metal at the joint of the brasses, in main- and side-rods, is generally about J of an inch. . The thickness k of metal between the pin and the butt end of the rods, and also the thickness of the flanges, are given in the following table : THICKNESS k (FIG. 469) OP METAL IN MAIN- AND SIDE-ROD BRASSES. Diameter of Cylinders. Thickness of Metal at *, Fig. 48V. Thickness of Flanges. 9" 4" r 10" t" i" 11" 1" ft" 12" J" " 13" i" i" 14" i" v 15" 16" *" i" i 17" l" " 18" l" *" 19" 20" 1" l" $ 21" H" r 22" H" \" The length of side-rods should be ascertained by actual measurement when the engine is hot. The brasses should have a somewhat loose fit on the crank-pins, so that, when the engine is in working order under steam, the side-rods can be moved on the crank-pin to just a perceptible extent. The following proportions of the different metals for main- and side-rod brasses we believe will give good satisfaction : Six pounds of copper, one pound of tin ; to one hundred pounds of this mixture add one-half pound of zinc and one-half pound of lead. CRANK-PINS. 336. Crank-pins are made either of steel or of the best quality of hammered iron. In order to reduce the wear on iron crank-pins, they are frequently case-hardened. During the process of case-hardening, the crank-pin will, to some extent, alter its form, and therefore, after case-hardening, it must be trued up. In so doing, the case-hard- ened surface may be reduced to an uneven thickness, which in time may produce an uneven wear, and interfere with the cool and smooth running of the engine. On the other hand, steel crank-pins do not need to be case-hardened, they wear well without it, and therefore the chances of obtaining a wearing surface of different degrees of hardness are lessened, and the causes of heating and uneven wear are to some extent removed. Yet a wrought-iron pin has an advantage over a steel one; the latter, when 318 MODERN LOCOMOTIVE CONSTRUCTION. subjected to excessive pressure which may happen even in the best designed engines may break or snap off suddenly, and thereby cause considerable damage ; on the other hand, a wrought-iron pin will bend to a greater extent before it breaks than a steel one, and consequently may give, in many instances, a timely warning of an excessive pressure, so that repairs or changes can be made before much damage has been done. But steel pins can resist a greater pressure than iron ones, and, since they do not need to be case-hardened, they are often preferred. Hence on some roads we find steel pins used exclusively, and on other roads iron pins are adopted. We prefer steel pins. 337. From the foregoing remarks we infer that in designing a crank-pin we must keep in view its strength, and also its liability of heating. To prevent heating, we must have a sufficient bearing surface, and, when a sufficient bearing surface has been provided, then the crank-pins, having such proportions as are adopted in modern locomotive practice, will also be strong enough for the work they have to do. Hence, in determining the dimensions of a crank-pin we shall be guided mostly by the pi'essure which the crank-pins have to resist. The pressure on the crank-pin is estimated by the pressure on its projected area ; that is to say, by the pressure on a rectangular surface, whose length and breadth are equal to the length and diameter of the crank-pin journal. In comparing the pressure per square inch of projected area of the crank-pins as made by different makers, we find a great difference; indeed, in some instances we find the pressure per square inch on the projected area to be about 1,000 pounds ; in other cases the pressure is nearly 2,000 pounds per square inch. The low pressures on crank-pins we find to occur mostly in small engines, and the higher pressures mostly in large engines ; which seems to indicate that the crank-pins in a number of small engines are somewhat large, and in a number of large engines the crank-pins are too small. The truth of these conclusions, we believe, is confirmed by experience and the results in practice. In the rules which are to follow, we shall adopt 1,600 pounds per square inch of projected area of the crank-pin, and determine the size of all crank-pins according to this pressure. CBANK-PINS FOR EIGHT-WHEELED PASSENGER ENGINES. 338. In designing a main crank-pin, care must be taken not to make its journals too long, because an increase of length will weaken the pin ; the diameters of the journals should not be larger than necessary, because enlarging the diameters will occasion a loss of work due to friction. Consequently, there should be a ratio between the diameter and the length of a locomotive crank-pin journal ; and this ratio can best be established by the proportions of crank-pins now in actual and successful service. In all locomotives which have more than one pair of drivers, the main crank-pins have two journals, as shown in Fig. 471. One of these journals is the main-rod journal ; the other is the side-rod journal. In wide-gauge (4 feet 8 inches) eight-wheeled passenger engines, the main-rod is nearly always placed next to the wheels; in narrow-gauge eight- wheeled passenger MODERN LOCOMOTIVE CONSTRUCTION. 319 Gui- lt is Fig. 471 engines we are frequently obliged to place the side-rod next to the wheel. If Fig. 471 iv|>rt>sfiits Ji crank-pin designed for an eight-wheeled passenger engine (4 feet 8 inches MI me), then the journal B will represent the main-rod journal ; and the journal C will represent the side-rod journal. The portion A of the pin which is pressed into the wheel is called the wheel fit. Let Fig. 471 represent a main crank-pin for an eight-wheeled passenger engine : it is required to find the diameter I) and the length L of the main-rod journal B ; it is also required to find the diameter d and the length I of the side-rod journal C. Let us commence by finding the dimensions of the main-rod journal B. first step will be to establish a ratio between its diameter D and its length L. not often that we find in eight- wheeled passenger engines a crank-pin in which the length of the main journal exceeds its diameter ; but there are a num- ber of eight-wheeled passenger engines in which the length and diameter of the main-rod journal are equal to each other; and lastly, we believe it is safe to say that, in the majority of engines, the diameter of the main journal is greater than its length. In the latter cases the ratio between the diameters and lengths, as made by different builders, varies some- what ; but good practice seems to indicate that the diameter of the main-rod journal should be about 1J times greater than its length. Occasionally crank-pins need to bo trued up a little, for which a small allowance should be made. Hence, in determining the dimensions of the main-rod journal, we shall first find its diameter and length, whose ratio is as 1J to 1, and then add, to allow for wear, about -fa to inch to the diameter thus found. We say ab&ut fa to inch, because the diameter determined by calculation will in many cases contain a fraction of an inch, and when this fraction does not contain even & inch, we shall then add a little less, or in some cases a trifle more, than inch, so as to make the fraction divisible by inch ; indeed, many locomotive builders do not adopt a diameter which cannot be divided by inch. If the diameter obtained by calculation contains even J inch, we simply add 4 inch for wear. When the length of the journal, as found by calculation, contains frac- tions which cannot be divided by inch, we simply take the nearest fraction divisible by it to that found; hence, in some cases the lengths adopted may be a little less, and in others a little greater than that found by calculation. For the sake of simplicity, we shall assume that the whole steam pressure on the piston is exerted to turn the wheels, allowing nothing for the friction of piston, etc.; we shall also neglect the pressure due to the obliquity of the main-rod. Now, since the pressure per square inch of projected area of a steel crank-pin journal is to be 1,600 pounds, we can readily find, under the foregoing conditions, this area when the steam pressure on the piston is known, thus: RULE 74. For crank-pins made of steel, divide the total maximum steam 320 MODERN LOCOMOTIVE CONSTRUCTION. pressure on the piston by 1,600 ; the quotient will be the number of square inches in the projected area of the main-rod journal for eight- wheeled passenger engines. Now, since the diameter of the journal is to be l times its length, we have the following rule : EULE 75. Multiply the projected area (as found by Eule 74) by 8, and divide the product by 9; extract the square root of the quotient; the result will be the length of the journal. Multiply this length by 1.125, and add for wear so as to make the diameter divisible by inch ; the sum will be the required diameter. EXAMPLE 108. Find the dimensions for the main-rod crank-pin journal for a passenger engine having cylinders 18 inches diameter ; maximum steam pressure per square inch of piston, 130 pounds. The area of an 18-inch piston is 254.47 square inches ; hence, the maximum steam pressure on the piston will be 254.47 x 130 = 33081.10 pounds. According to Eule 74, the number of square inches in the projected area of the main-rod journal will be 33081.10 = 20.67 square inches. According to Eule 75, we find the length to be 8 x 20.67 . 00 . , ^- - = 4.28 inches. t7 And the diameter we find to be 4.28 x 1.125 = 4.815 inches; adding to this diameter .06 (which in this case is a little less than ^ inch), we obtain 4J inches. Hence, the diameter of this journal should be 4J inches, and its length, 4J inches. 339. To determine the dimensions of the side-rod journal we proceed in manner similar to that adopted for finding the dimensions of the main journal. Our first step will be to compute the projected area. In good practice we find that in eight- wheeled passenger engines the projected area of the side-rod journal is equal to about 65 to 75 per cent, of that of the main-rod journal ; we believe that about 67 per cent, is a good proportion. Hence, when we know the projected area of the main-rod journal, that of the side-rod journal may be found by making it equal to about 67 per cent, of the former. But this result can be obtained in a more direct way by the following rule, which will give results agreeing well with the average good practice. EULE 76. For steel crank-pins, divide the maximum pressure on the piston by 2,400 ; the quotient will be the number of square inches in the projected area of a side- rod journal for eight-wheeled passenger engines. In many locomotives we find the length of the side-rod journal to be equal to its diameter ; on the other hand, we find as many, if not a greater number of engines, in which the diameter of the side-rod journal is greater than its length. In the latter class, the ratio between the diameters and lengths, as made by different makers, varies somewhat, but good practice seems to indicate that this ratio should !.(><< >Morni: i-o\sri;i <-THI\. 321 be equal to that of the main-rod journal, namely, the diamter should be l times greater than the length; and these porportions we shall adopt. To the diameter thus found we shall also add ^ to inch, so as to avoid fractious which cannot be divided by & inch. As for the length of the side-rod journals, we .shall simply adopt such as can be divided by inch, and which will be the nearest to the fraction found by calculation, and therefore may in some cases be a little less and in others greater than that obtained by the rule. RULE 77. To find Ihe length and diameter of a steel side-rod journal for eight- wheeled passenger engine. Multiply the projected area of the side-rod journal (as found by Eule 76) by 8, and divide the product by 9; extract the square root of the quotient ; the result will be the required length. Multiply the length by 1.125, add to the product from ^ to inch, so as to obtain a numerical value divisible by & inch ; the suni will be the required diameter. . EXAMPLE 109. Find the dimensions for the side-rod journal for a passenger engine having cylinders 18 inches diameter; maximum steam pressure per square inch of piston, 130 pounds. We have already found, in Example 108, that the maximum steam pressure on the piston is 33081.10 pounds ; hence, according to Rule 76, we have 33081.10 ., , , = 13.78 square inches, which is the projected area of the side-rod journal. According to Rule 77, the length should be v 7 ' 8 x 13.78 9 = 3.49 inches. For the diameter we have 3.49 x 1.125 = 3.926 inches ; to this add .199 inch ; the sum will be 4.1 25, which is the required diameter; hence, the side-rod journal should be 4 inches diameter, and 3 inches long. In this manner the diameters and lengths of steel crank-pins given in the follow- ing tables have been obtained. TABLE 37. PI.MEXSIOXS OK STEEL CKAXK-1'IX JOl'IiXALS FOB EIGHT-WHEELED PASSEXOEU ENGINES (FOUE WHEELS COXXEiTEPi. MAXIMT.M STEAM PKESSI'KE OX THE PISTON, Il!!> POUNDS PER SQUARE INCH. LETTERS AT THE HEAD OF rol.l'MXs KEFEK TO FIG. 471. Main-rod Journals. Side-rod Journals. Diameter of Cylin- ders. Diameter D Length Diameter d Length 9 .1 If 10 a 2* 11 11 21 2i 21 . 2 12 2} 2* 2t 13 3* 3 2* 2* 14 31 3* 3* q 15 4 3i at 2J 16 4i w 3* 3 17 4* 3i 31 34 is 4} 44 3J 31 19 :. *f 4* 3* ta i *l 31 322 MODERN LOCOMOTIVE CONSTRUCTION. TABLE 38. DIMENSIONS OF STEEL CRANK-PIN JOURNALS FOR EIGHT-WHEELED PASSENGER ENGINES) FOUR WHEELS CONNECTED). MAXIMUM STEAM PRESSURE ON THE PISTON, 130 POUNDS PER SQUARE INCH. LETTERS AT THE HEAD OF COLUMNS REFER TO FIG. 471. Dinmeter of Cylin- Main-rod Journals. Side-rod Journals. ders. Diameter 2> Length L Diameter d Length 9 84 24 24 U 10 at 2| 2i 2 11 3* 2* 24 24 12 3| 21 2i 2| 13 Bf 34 21 24 14 31 31 34 2f 15 4 34 3| 3 16 41 34 3* 34 17 *j 4 31 3f 18 41 4i 44 34 19 54 44 4i 4 20 ii 4f 44 31 TABLE 39. DIMENSIONS OF STEEL CRANK-PIN JOURNALS FOR EIGHT-WHEELED PASSENGER ENGINES (FOUR WHEELS CONNECTED). MAXIMUM STEAM PRESSURE ON THE PISTON, 140 POUNDS PER SQUARE INCH. LETTERS AT THE HEAD OF COLUMNS REFER TO FIG. 471. Main-rod Journals. Side-rod Journals. Diameter of Cylin- ders. Diameter D Length Diameter a Length 9 2f 2i 24 10 21 24 2f 2 11 34 24 2| 8f 12 34 3 21 24 13 34 3 34 H 14 4 34 3i 21 15 4i 3| 34 3 16 4f 4 34 3i 17 41 4i 4 34 18 54 44 4* 31 19 51 4* 44 31 20 5* 41 4* 4 TABLE 40. DIMENSIONS OF STEEL CRANK-PIN JOURNALS FOR EIGHT-WHEELED PASSENGER ENGINES (FOUR WHEELS CONNECTED). MAXIMUM STEAM PRESSURE ON THE PISTON, 150 POUNDS PER SQUARE INCH. LETTERS AT THE HEAD OF COLUMNS REFER TO FIG. 471. Main-rod Journals. Side-rod Journals. Diameter of Cylin- ders. Diameter D Length L Diameter d Length 9 21 2f ai 11 10 3 2* 24 24 11 3 21 2} 2J 12 Bl 34 3 24 13 31 3f 34 2* 14 44 3f 3f 3 15 44 31 81 3J 16 44 44 31 3i 17 5 4| 44 34 18 BJ *f 4| 3} 19 Bf 41 4f 4 20 51 54 44 44 LOCOMOTIVE COXSTRUCTIOX. 323 TABLE 41. DIMKXSFONS OP STEEL CRANK-PIN JOURNALS FOR EIGHT-WHEELED PASSENGER ENGINES (FOUR WHEELS oiNNKtTKlM. MAXIMUM STEAM PRESSURE ON THE PISTON, 160 POUNDS PER SQUARE INCH. LETTERS AT THE HEAD OF COLUMNS REFER TO FIG. 471. Main-rod Journals. Side-rod Journals. T>i m tpr nf Cvlln (U-re. Diameter D Length Diameter d Length B 2* 2t 24 2 10 3* -'- 24 24 11 3f -: 2* 2t 12 3f 34 3 2* 13 4 34 34 2J H 44 3J 34 3 15 44 4 3* 34 16 4| H 4 34 17 54 *i 44 3f 18 Bj 4J 44 34 19 H 5 4f 44 20 64 5i 5 4| 340. Fig. 472 represents a rear crank-pin for an eight-wheeled passenger engine ; in fact, this figure and Fig. 471 represent a pair of crank-pins for an engine of this class. Figs. 474, 475 represent another pair of crank-pins for the same class of engine ; they were made of steel, and designed for an engine having cylinders 17 inches diame- ter. Fig. 474 represents the main, and Fig. 475, the rear crank-pin ; their forms, as will be seen, differ somewhat from those of the pins previously referred to. The general practice is to make the diameter of the outer collar (see Fig. 471) from 1 to l inches greater than the diameter d of the journal C; the diameters of the middle collar and the collar next to the hub of the wheel are generally made 1J inches greater than the diameter D of the journal 7?. The thickness h of the outer collar is generally J inch, sometimes f inch. The thickness g of the middle collar, and the thickness/ of the collar next to the hub of the wheel, will depend upon the distance between the line coinciding with the axis of the cylinder and the face of the hub of wheel. In many eight-wheeled passenger engines the thickness g is J inch, and the thickness/ 3 inch. Sometimes the hub of the wheel is made exceedingly deep, leaving no room for a collar next to the hub; in such cases the main crank-pin will appear as shown in Fig. 474. The diameter of the wheel fit of this crank-pin is made comparatively great, so as to obtain a shoulder against which the brasses of the main-rod can bear; this shoulder generally projects ^ of an inch beyond the face of the hub. The junctions / / <>' the journal and the face of the collars (Fig. 471) should in every instance be curved surfaces turned to a radius of | inch for small crank-pins, and increased up to a radius of J inch for large pins. For many rear crank-pins the shank E is formed so as to leave a collar next to the hub of the wheel, as shown in Fi^. 47 The diameter n of this collar is made equal to that of the corresponding one on the main crank-pin, and its thickness p is generally | or ? inch. Tin- iliann-tfi- /// of the shank E is generally made from \ to J inch greater than the diameter D of the main-rod journal. 324 MODERN LOCOMOTIVE CONSTRUCTION. Fig. 473 also represents a rear crank-pin for an eight-wheeled passenger engine. The shank E of this pin has a uniform taper nearly throughout its whole length ; the diameter n is made as the diameter n of the collar of the shank in Fig. 472 equal to the diameter of the collar on the main crank-pin ; that is, the collar next to the hub. Making the form of the shank like that shown in Fig. 473 increases the weight of the pin unnecessarily ; it does no good, and therefore this form of shank is not recom- mended. Indeed, in order to reduce the weight of the rear crank-pin, some locomotive builders make its shank E like that shown in Fig. 479 ; this rear crank-pin has a collar on each side of the journal, and the diameter r, next to the inner collar, is generally made | of an inch greater than the diameter d of the journal. Figs. 476, 477 also represent a pair of crank-pins for an eight-wheeled passenger MODERX LOCO.MOTITK CONSTRUCTION. 325 having cylinders 17 inches diameter. It will be noticed that the shank E of the rear crank-pin, Fig. 47(5, is different in form from those previously shown. Here the diameter s, in the center of the shank, is made less than the diameter k, or the diameter of the wheel fit. The object of this design of crank-pin is to reduce its rigidity, so that when the crank-pin is subjected to a sudden stress or shock, the slight flexibility which it may possess will lessen the effect of the shock, and thus reduce the chances of breaking. Of course, the proportions of this crank-pin must be such that none of its fibers will be strained beyond the limits of elasticity. These crank-pins are used to quite an extent on one of our prominent roads, and give good satisfaction. On other roads this form of crank-pin is seldom found. The reason why this form is not generally adopted is probably on account of the difficulty of determining its correct proportions ; in fact, these proportions are generally obtained by a tentative process rather than by computation, Figs. 478, 479 represent a pair of crank-pins for an eight-wheeled passenger engine with cylinders 17 inches diameter ; they are also often used for the same class of engines with cylinders 18 inches diameter. These crank-pins are designed for engines which have solid-ended side-rods. One of these rods is shown in Fig. 41!). ,'!41. In eight-wheeled passenger engines the diameter of the wheel fit of the rear crank-pin is always made equal to that of the main crank-pin. This diameter should never be made less than the diameter I) uf the journal next to the wheel; in fact, we believe it to be good practice to make the diameter of the wheel fit from to 4 inch greater than the diameter I). 326 MODERN LOCOMOTIVE CONSTRUCTION. When the crank-pin has a collar next to the wheel, the jtmction of the wheel fit and the face of the collar should never be a sharp corner, but should be well rounded out. The crank-pins are generally pressed into the wheels. When the crank-pin hole is perfectly true and smooth, the pin should be pressed in with a press- F ig. 480 ure equal to about six tons for every inch in diameter of the wheel fit. When the hole is not perfectly true, which may be the result of shrinking the tire on the wheel center after the hole for the crank-pin has been bored, or if the hole is not perfectly smooth, the pressure may have to be increased to nine tons f or every inch in diameter of the wheel fit. From these remarks it appears that it is always best to shrink the tires on the wheel centers before the holes for the crank-pins are bored. 342. Fig. 480 represents another form of crank-pin used for solid-ended side-rods ; it differs from that shown in Fig. 479 in the fact that it has no loose collar for holding the side-rod in position after the latter has been slipped on to the journal ; instead of a loose collar a groove a is turned into the journal near the end. The design of side-rod used for this pin is shown in Figs. 481 ,and 482. A solid brass bushing is forced into MODERN LOCOMOTIVE CONSTRUCTION. 327 the end of the side-rod; a brass plate B made in two pieces is made to fit into the groove a in the crank-pin journal ; a brass cap C covers the end of the pin ; four bolts I) D extend through the whole width of this side-rod end and hold the cap C and the W ~, ...; L " v '5 1 1 i plate B firmly in position, and also provont the brass bushing from turning around should it become loose through constant service. The bolt-heads are countersunk into the flange of the bushing, as shown in Fig. 483. Fig. 483 represents in detail the brass bushing A ; Fig. 484 represents the brass plate B; and Fig. 485 represents the brass cap C; these require no further explanation. 328 MODERN LOCOMOTIVE CONSTRUCTION. MAIN CRANK-PINS FOR MOGUL, TEN-WHEELED, AND CONSOLIDATION ENGINES. 343. In ten-wheeled, Mogul, and consolidation engines, the arrangement of the side- and main-rods generally differs from the arrangement of the rods in passenger engines. In the latter class of engines we have seen that the main-rod takes hold of the inner journal of the main crank-pin ; in the former classes of engines the main-rod generally takes hold of the outer journal of the main crank-pin, thus bringing the side- rods next to the wheels. Fig. 487 represents a main crank-pin for a consolidation engine having cylinders 20 inches diameter ; and Fig. 486 represents one of the side-rod pins for the same engine. The main crank-pins for consolidation, Mogul, and ten-wheeled engines are generally simi- lar in form ; hence the rules by which the dimensions of the crank-pin journals for one of these classes of engines are deter- mined can also be used for finding the dimensions of similar crank-pin journals for the other two classes of engines. The following rules are for steel pins. In establishing these rules we shall again be guided by the dimensions of the crank-pins at present in use, and which give good satisfaction. Let us commence with the main-rod journal on the main crank-pin ; this joiirnal will be the outer one in Fig. 487 ; it is required to find the diameter D and the Fig. 486 Fig. 487 length L. In Art. 337 it has been stated that, to prevent a locomotive crank-pin from heating, it must have a sufficient bearing surface, and when such has been provided, the crank-pin will also be strong enough for the work it has to do. These remarks again apply to the main-rod journal of the crank-pins, in which this journal is the outer one, as shown in Fig. 487 ; they also apply to the side-rod crank-pin, such as is shown in Fig. 486 ; but they do not apply to side-rod journal on the main crank- pins, as will presently be seen. Since the pressure per square inch of the projected area of a steel crank-pin journal should not exceed 1,600 pounds, we readily find, by Eule 74, the projected area of the main-rod journal for consolidation, Mogul, and ten-wheeled engines. Thus : MODERN LOCOMOTIVE CONSTRUCTION. 399 EXAMPLE 110. What should be the projected area of the main-rod journal on the main crunk-pin for a Mogul engine having cylinders 18 inches diameter? Maximum steam pressure on the piston is 130 pounds per square inch. Multiplying the area in square inches of the piston by the steam pressure per square inch, we have 254.47 x 130 = 33081.10 pounds, which is the maximum steam pressure on the piston. According to Rule 74, we have 33081.10 . . = 20.67 square inches, which is the projected area of the main-rod crank-pin journal. Before we can find the diameter and the length of this journal we must establish a ratio between the diameter and the length. There are a few engines of the classes now under consideration in which the diameter of the main-rod crank-pin journal exceeds its length ; and on the other hand we meet with a few engines in which the diameter is less than the length. But in a large majority of these engines the diame- ter of the main-rod crank-pin journal is equal to its length. We shall therefore adopt a rule by which we can find the diameter and the length which are equal to each other. To the diameter so found we shall add, for wear, about iV or inch, so as to obtain such diameters whose fractions, if they have any, are divisible by inch ; as for the length, we shall adopt the nearest which contains fractions that can be divided by J inch, and this may be either a little less or a little greater than the length found by the following rule : RULE 78. To find the diameter and length of the main-rod crank-pin journal : Extract the square root of the projected area, as found by Rule 74. If this square root does not contain any fractions, or if it does contain fractions which can be divided by i inch, add to it i of an inch for wear ; the sum will be the diameter. If the square root contains fractions which cannot be divided by J inch, add ^ or a little more, so as to obtain diameters which are divisible by inch. The square root of the projected area will also be the length of the pin ; if it is not divisible by inch, adopt the near- est length which is divisible by & inch. EXAMPLE 111. Find the diameter and length of the main-rod crank-pin journal for a Mogul engine having cylinders 18 inches diameter, maximum steam pressure on piston 130 pounds per square inch. In Example 110 we have found that the projected area of this journal is 20.67 square inches. The square root of 20.67 is 4.54 inches, which is a little more than 4 inches, hence the diameter is 4g inches ; and the length is 4J inches. 344. The projected area of the side-rod journal of the main crank-pin, that is, the inner journal in Fig. 487, as made by different builders, varies somewhat ; hence we find that in a number of engines the projected area of the side-rod journal is greater than that of the main-rod journal ; and in a number of engines it is less; but in the majority of engines the projected areas of the two journals are equal, and these lalter proportions we shall adopt. Hence the projected area of the side-rod journal of the main crank-pin is found by Rule 74. 330 MODERN LOCOMOTIVE CONSTRUCTION. True, if we had only to make provisions for the prevention of heating, a smaller area would suffice, but, since the outer journal of this pin is subjected to a greater pressure than is brought to bear on the side-rod journal, and since the pressure on the outer pin acts with a leverage, we require a large projected area so as to provide for the strength of the pin. The ratio between the diameter and length of this side-rod journal, as made by different builders, also varies ; but the most common practice is to make the diameter 1J times larger than the length; and these proportions we shall adopt. We have therefore the following rule : RULE 79. To find the length and diameter of the side-rod journal for the main crank-pin, when this journal is next to the wheels, divide the projected area, as found by Rule 74, by 5 ; multiply the quotient by 4, and extract the square root from the product ; this square root will be the length of the side-rod journal. If this length is not divisible by inch, adopt the nearest one which can be divided by inch. For the diameter multiply the square root found as above by 1.25 ; if this product is divisible by ^ inch, add to it | inch for wear ; the sum will be the required diameter ; if this product is not divisible by J-, add from tV to inch, so as to make it divisible by inch ; the sum will be the required diameter. EXAMPLE 112. Find the length and diameter of the side-rod journal for the main crank-pin for a Mogul engine having cylinders 18 inches diameter ; maximum steam pressure on the piston, 130 pounds per square inch. The projected area of this journal is, according to Rule 74, 20.67 square inches ; in fact, this area we have found in Example 110. According to Rule 79, we have "*> * * = 16.53. 5 The square root of 16.53 is V16.53 = 4.06 inches. Hence the length of this journal is 4 inches. Again, for the diameter we have 4.06 x 1.25 = 5.07 inches, which is a little more than 5 inches ; hence the diameter of this journal is 5 inches. In a similar way we can determine the dimensions of the journals for any main crank-pin (made of steel) under different pressures for ten-wheeled, Mogul, and con- solidation engines. The dimensions of the main crank-pin journals given in the following tables have been computed by the foregoing rules. MODERN LOCOMOTIVE CONSTRUCTION. TABLE 42. 331 DIMENSIONS OF THE MAIN CRANK-PIN JOURNALS (STEEL) FOR MOGUL, TEN-WHEELED, AND CONSOLIDA- TION ENGINES. MAXIMUM STEAM PRESSURE ON THE PISTON, 120 POUNDS PER SQUARE INCH. Diameter of Cylin- ders. Main-rod Journals. Side-rod Journals. Diameter. Length. Diameter. Length. 9 24 inches. 24 inches. 24 inches. 2 inches. 10 24 2f 2t 24 11 21 y 3 2| 12 3 21 3f 13 34 34 3f 21 14 34 3f 31 3 15 3t 3 44 31 16 4 31 44 34 17 4i 4* 4* 3f 18 44 4f 5 31 19 4} 4* 54 44 20 5 4* 54 4| 21 54 54 H 44 22 5* 5f 6 4* TABLE 43. DIMENSIONS OP THE MAIN CRANK-PIN JOURNALS (STEEL) FOR MOGUL, TEN-WHEELED, AND CONSOLIDA- TION ENGINES. MAXIMUM STEAM PRESSURE ON THE PISTON, 130 POUNDS PER SQUARE INCH. Diameter of (rylin- den. Main-rod Journals. Side-rod Jonrnale. Diameter. Length. Diameter. Length. 9 2{ inches. 2J inches. 2| inches. 2 inches. 10 24 21 24 11 21 21 34 24 12 34 3 34 21 13 3f 34 31 3 14 3i 34 4 34 15 31 3} 44 3f 16 44 4 4* 3* 17 4* 44 *1 31 18 i 44 54 4 19 41 41 54 44 20 54 5 5f 44 21 Sf 54 6 4} 22 5 54 64 5 TABLE 44. DIMENSIONS OF THE MAIN CRANK-PIN JOURNALS (STEEL) FOR MOGUL, TEN-WHEELED, AND CONSOLIDA- TION ENGINES. MAXIMUM STEAM PRESSURE ON THE PISTON, 140 POUNDS PER SQUARE INCH. Diameter of Cylin- ders. Main-rod Journals. Side-rod Journal*. Diameter. Length. Diameter. Length. 9 24 inches. 2} inches. 21 inches. 24 inches. 10 2} 1 2* 3 11 3 < 21 34 24 12 34 34 3| 2} 13 34 3* 31 3 14 31 3| 44 34 15 4 31 44 34 16 44 44 41 31 17 44 4 5 4 18 41 4| 5f 44 19 r>4 5 5* 44 20 5f 54 51 4t 21 5t 54 64 41 22 51 51 64 54 332 MODERN LOCOMOTIVE CONSTRUCTION. TABLE 45. DIMENSIONS OF THE MAIN CRANK-PIN JOURNALS (STEEL) FOR MOGUL, TEN-WHEELED, AND CONSOLIDA- TION ENGINES. MAXIMUM STEAM PRESSURE ON THE PISTON, 150 POUNDS PER SQUARE INCH. Diameter of Cylin- ders. Main-rod Journals. Side-rod Journals. Diameter. Length. Diameter. Length. 9 24 inches. 2f inijhes. 2f inches. 24 inches. 10 H It 34 24 11 34 3 3| 24 12 3f 3* 3J 24 13 34 34 4 34 14 3J 34 *i 3f 15 44 4 *4 34 16 4f 41 3* 17 4| 4* BJ 44 18 5 4* 51 4f 19 5* 8* Bf 44 20 54 5f 64 H 21 Bf 54 6| 54 22 64 6 64 5f TABLE 46. DIMENSIONS OF THE MAIN CRANK-PIN JOURNALS (STEEL) FOR MOGUL, TEN-WHEELED, AND CONSOLIDA- TION ENGINES. MAXIMUM STEAM PRESSURE ON THE PISTON, 160 POUNDS PER SQUARE INCH. Diameter of Cylin- ders. Main-rod Journals. Side-rod Journals. Diameter. Length. Diameter. Length. 9 24 inches. 24 inches. 2| inches. 2J inches. 10 2J 2f 3 24 11 34 3 34 2f 12 31 3f 3J 3 13 3f 34 44 3i 14 4 34 44 34 15 4* 44 4J 3i 16 *i 4| 54 4 17 *i 4* 54 4t 18 54 5 5t 44 19 BJ 5f 6 4i 20 51 54 6| 5 21 6 51 64 54 22 61 64 7 54 There are very few Mogul engines built with cylinders 9 inches diameter, and we do not know of any consolidation engines with cylinders of such small diameter; it may therefore appear unnecessary to extend the tables to such small cylinders. But we have seen that, in narrow-gauge passenger engines, the side-rods are often placed next to the driving wheels ; these engines generally have small cylinders, consequently these tables are useful for obtaining the dimensions of main crank-pins for this class, and other classes of engines whose side-rods are placed next to the driving wheels. SIDE-ROD PINS FOE TEN-WHEELED AND MOGUL ENGINES. 345. In comparing the side-rod pins for ten-wheeled and Mogul engines with the side-rod pins for eight-wheeled passenger engines whose cylinders are equal in size to those in the former classes of engines, and all subjected to the same steam pressure, MODERN LOCOMOTirE CONSTRUCTION. 333 we find that the side-rod pins in ten-wheeled and Mogul engines are smaller than those in eight-wheeled passenger engines. The reason for this is that in passenger engines we have only two driving wheels on each side, and in ten-wheeled and Mogul engines we have three driving wheels on each side. With cylinders of equal size, and equal steam pressures, the thrust on the main-rod crank-pin journals in all the different classes of engines will be practically equal. Now assuming that the total weight on the driving wheels is equally distributed, the pressure on the side-rod pins in ten- wheeled and Mogul engines must be less than that on the side-rod pins in passenger engines, because in the latter class nearly all the pressure on the main pin is transmitted to two wheels, whereas, in the former class an equal amount of pressure is transmitted to three wheels. Hence, the rules previously given for determining the dimensions of the side-rod pin for eight-wheeled passenger engines are not suitable for finding the dimensions of the side-rod pins for ten-wheeled and Mogul engines. The following rules will give results which agree closely with the average good practice : KULE 80. Divide the total steam pressure on the piston by 2,800 ; the quotient will be the number of square inches in the projected area of steel side-rod pins in the front and rear driving wheels under ten-wheeled and Mogul engines. RULE 81. To find the diameter and length of the front and rear side-rod pins in the above classes of engines, extract the square root of the projected ai'ea, as found by Rule 80. If this square root does not contain any fractions, or if it does contain fractions which can be divided by inch, add to it inch for wear ; the sum will be the diameter of the pins. If the square root contains fractions which cannot bo divided by inch, add about -fa inch, or a little more, so as to obtain diameters which are divisible by J inch. The square root of the projected area will also be the length of the pins; if it is not divisible by inch, adopt the nearest length which is divisible by i inch. EXAMPLE 113. Find the diameter and length of the front and rear side-rod pins in a Mogul engine having cylinders 18 inches diameter ; maximum steam pressure on the piston, 130 pounds per square inch. The total steam pressure on the piston is equal to its area multiplied by the steam pressure per square inch ; therefore, 254.47 x 130 = 33081.10 pounds = total pressure on the piston. According to Rule 80, the projected area is equal to 33081.10 9800 : 11.81 square inches. According to Rule 81, we must find the square root of 11.81, which is 3.43, or, we may say it is practically equal to 3^$ inches; hence, the diameter of this pin is 3 inches and its length 3fj inches. In a similar manner the dimensions of steel side-rod pins for ten-wheeled and Mogul engines in the following tables have been computed : 334 MODERN LOCOMOTIVE CONSTRUCTION. TABLE 47. DIMENSIONS OF STEEL SIDE-BOD PINS IN THE FRONT AND REAR WHEELS FOR TEN- WHEELED AND MOGUL ENGINES. .MAXIMUM STEAM PRESSURE ON THE PISTON, 120 POUNDS PER SQUARE INCH. Diameter of Cylinders. Diameter of Journals. Length of Journals. 9 14 inches. 1} inches. 10 2 ' 14 " 11 2* ' 2 " 12 2| ' 2* " 13 2* ' 2| " 14 2f ' 21 " 15 24 ' 2f " 16 34 ' 3 17 3i ' 34 " 18 34 " 3| " 19 3$ " 3| " 20 3f " 3f " 21 4 " 34 " 22 44 " 4 " TABLE 48. DIMENSIONS OF STEEL SIDE-ROD PINS IN THE FRONT AND REAR WHEELS FOR TEN-WHEELED AND MOGUL ENGINES. MAXIMUM STEAM PRESSURE ON THE PISTON, 130 POUNDS PER SQUARE INCH. Diameter of Cylinders. Diameter of Journals. Length of Journals. 9 14 inches. If inches 10 2 14 " 11 2 " 24 " 12 2| | 2J " 01 It 13 *^8 ^4 14 2f ' 2f " 15 3 ' 24 ' 16 34 ' 3 ' 17 3f ' 3 ' 18 34 ' 3f ' 19 3} ' 3* ' 20 34 3f ' 21 44 ; 4 22 4 4i TABLE 49. r * DIMENSIONS OF STEEL SIDE-ROD PINS IN THE FRONT AND REAR WHEELS FOR TEN-WHEELED AND MOGUL ENGINES. MAXIMUM STEAM PRESSURE ON THE PISTON, 140 POUNDS PER SQUARE INCH. Diameter of Cylinders. Diameter of Journals. Length of Journals. 9 14 inches. If inches. 10 24 " 2 " 11 2i " 24 ' 12 1>4 " 21 ' 13 '1$ " 24 ' 14 24 " 2f ' 15 34 " 3 ' 16 3i " 34 ' 17 34 " 3| ' 18 3f " 34 ' 19 34 " 3f ' 20 44 " 4 21 4i " 44 " 22 4| " 4| " MODERN LOCOMOT/rt; COXSTRVCTIOX. 335 TABLE 50. DDffiNSIONS OP STEEL SIDE-BOD PINS IN THE FRONT AND REAR WHEELS FOR TEN-WHEELED AND MOGUL ENGINES. MAXIMUM STEAM PRESSURE ON THE PISTON, 150 POUNDS PER SQUARE INCH. Diameter of Cylinders. Diameter of Journals. Length of Journals. 9 2 inches. H inches. 10 2i " 2 11 24 ' 2J " 12 2* ' 2i ' 13 2t ' 24 " 14 3 ' 2* " 15 3* ' 3 " 16 3f ' 3* ' 17 34 ' 3i 18 3f " 34 ' 19 4 " 3J ' 20 4i " 44 ' 21 4i " 4| 22 44 " 44 ' TABLE 51. DDIENSIONS OF STEEL SIDE-ROD PINS IN THE FRONT AND REAR WHEELS FOR TEN-WHEELED AND MOGUL ENGINES. MAXIMUM STEAM PRESSURE ON THE PISTON, 160 POUNDS PER SQUARE INCH. Diameter of Cylinders. Diameter of Journals. Length of Journals. 9 2^ inches. 2 inches. 10 2i " 24 " 11 24 " 2| " 12 24 " 24 " 13 2* " 2f ' 14 34 " 3 ' 15 3 " 34 ' 16 34 " 31 ' 17 3| " 3+ ' 18 3J " 3J ' 19 4* " 4 " 20 4! 4i " 21 41 " 44 " 22 4f " 44 " SIDE-BOD PINS FOR CONSOLIDATION ENGINES. 346. In the foregoing article we have seen that the side-rod pins for eight-wheeled passenger engines are larger than those for Mogul and ten-wheeled engines. If, now, we compare the relative pressures on the side-rod pins in Mogul and consolidation engines, we will find that for the latter class of engines we may make the side-rod pins still smaller ; that is, say, they may be made smaller than those in Mogul engines. The reason for this will be seen by referring to Fig. 488, which shows the arrange- ments of the driving wheels on one side of a consolidation engine. The main-rod pin is marked M, and A, B, D are the side-rod pins. For the purpose of comparison, we may assume that in all locomotives the total weight on the drivers is equally distributed on the wheels; and we may also assume that the whole pressure on the main-rod crank-pin journal is required for turning the wheels (this, of course, is not exactly true). Under these conditions it will require one-fourth of the pressure on the main crank-pin 336 MODERN LOCOMOTIVE CONSTRUCTION. journal to turn each wheel. In Mogul engines we have only three driving wheels on each side of the engine ; and with cylinders of the same size as those in a consoli- dation engine, and also equal steam pressures, the thrust on the main-rod crank-pin journal will practically be the same in both engines ; and the pressure on the side-rod Fourth Vair of Drivers Third Pair of Drivers Second Fatr of Drivers First Pair of Drivers Centrt of Slain Hod M Fig. 488 pins for Mogul engines will be equal to one-third of that on main-rod journal instead of one-fourth, as in consolidation engines. Therefore, since the pressure on the side- rod pins in the latter class of engines is less than that in the former classes, it follows that the side-rod pins for consolidation engines may also be reduced in size. True, these pins are subjected to other pressures besides that due to pressure on the piston ; but these may be provided for by choosing a proper divisor for the total steam pressure on the piston in determining the projected area, as we have done in the following rule : RULE 82. Divide the total maximum steam pressure on the piston by 3,200; the quotient will be the number of square inches in the projected area of any one of the steel side-rod pins A, B, D (Fig. 488) for consolidation engines. The length and diameter of these pins are equal, or nearly so, in the majority of engines of this class ; hence the following rule : RULE 83. To find the length and diameter of steel side-rod pins for consolidation engines, extract the square root of the projected area as found by Rule 82 ; result will be the length of the pin ; if this length contains a fraction not divisible by inch, then adopt the nearest length which can be divided by inch. For the diameter, add to the length found inch for wear ; the sum will be the required diameter. EXAMPLE 114. Find the dimensions of the side-rod pins for a consolidation engine having cylinders 20 inches diameter ; maximum steam pressure on the piston, 130 pounds per square inch. The area of a piston 20 inches diameter is 314.16 square inches; hence the maximum steam pressure on the piston will be 314.16 x 130 = 40840.8 pounds. 40840 8 According to Rule 82, we have Qonf - = 12.76 square inches, which is the projected area of the pin. The square root of 12.76 is 3.57. Hence, the length of the side-rod pin will be 3 inches, and its diameter will be 3 inches. The dimensions given in the following tables have been computed by the fore- going rules. There is a possibility, when a consolidation engine is running over an uneven track, causing the wheels to run out of alignment, that the side-rod pin B will be subjected to a greater pressure than the side-rod pins A and D. Consequently, we frequently find the side-rod pin B made from i to of an inch greater in diameter than that of the pins A and D. This is good practice, but not a universal one, as in many LOCOMOTIVE CONSTRUCTION. 337 engines all the side-rod pins are the same size. In computing the dimensions given in these tables, we have assumed that all the side-rod pins should be equal in size. If it is desirable to increase the size of the pin B, its diameter only should be increased ; the length should remain as given ; by so doing the center lines of the side- rods can be kept more readily in the same vertical plane, which is of importance. TABLE 52. DIMENSIONS OF STEEL SIDE-ROD PINS FOR CONSOLIDATION ENGINES. MAXIMUM STEAM PRESSURE ON THE PISTON, 120 POUNDS PER SQUARE INCH. Diameter of Cylinder*. Diameter of Journals. Length of Journals. 14 24 inches. 2} inches. 15 24 " 24 " 16 24 " 2} " 17 3 " 24 " 18 34 " 3 " 19 3| " 3J " 20 3f " 34 " 21 31 " 3f " 22 34 " 3f " TABLE 53. DIMENSIONS OF STEEL SIDE-ROD PINS FOR CONSOLIDATION ENGINES. MAXIMUM STEAM PRESSURE ON THE PISTON, 130 POUNDS PER SQUARE INCH. Diameter of Cylinders. Diameter of Journals. Length of Journals. 14 2f inches. 24 inches. 15 2J " 2f " 16 3 " 24 " 17 34 " 3 " 18 3f ' 34 " 19 34 ' 3f " 20 3f ' 31 " 21 34 ' 3f " 22 44 ' 4 " TABLE 54. DDIENSIONS OK STEEL SIDE-ROD PINS FOR CONSOLIDATION ENGINES. MAXIMUM STEAM PRESSURE ON THE PISTON, 140 POUNDS PER SQUARE INCH. Diameter of Cylinders. Diameter of Journals. Length of Journals. 14 -: inches. 24 inches. 15 24 " 2f " 16 3* ' 3 " 17 34 ' 34 " 18 34 ' 3| " 19 31 ' 34 " 20 3t ' 3* " 21 4 34 " 22 44 " 44 " 338 MODERN LOCOMOTIVE CONSTRUCTION. TABLE 55. DIMENSIONS OF STEEL SIDE-ROD PINS FOR CONSOLIDATION ENGINES. MAXIMUM STEAM PRESSURE ON THE PISTON, 150 POUNDS PER SQUARE INCH. Diameter of Cylinders. Diameter of Journals. Length of Journals. 14 2f inches. 2| inches. 15 3 2* 16 34 3 17 3| 3i 18 3f 8* 19 3f 3| 20 4 3J 21 44 4 22 4f *J TABLE 56. DIMENSIONS OF STEEL SIDE-ROD PINS FOR CONSOLIDATION ENGINES. MAXIMUM STEAM PRESSURE ON THE PISTON, 160 POUNDS PER SQUARE INCH. Diameter of Cylinders. Diameter of Journals. Length of journals. 14 2| inches. 2J inches. 15 34 3 ' 16 3i 34 ' 17 34 3| 18 3* 34 19 3J 8| 20 44 4 21 4i 44 22 44 4f WHEEL FITS. We have seen that in eight-wheeled passenger engines (two driving wheels on each side) the diameter of the wheel fit of the side-rod pin is equal to that of the main pin. In ten-wheeled, Mogul, and consolidation engines, the diameter of the wheel fit of the side-rod pins is less than that of the main pin ; it is generally from i to inch greater than the diameter of the journal. The wheel fit for the main pin should never be less than the diameter of the journal next to the wheels ; in fact, it is better practice to increase it from to J inch. KNUCKLE JOINTS. 347. The side-rods in all locomotives which have more than two driving wheels on each side have a knuckle joint ; its form in many engines is similar to that shown in Figs. 489 and 490. In Mogul and ten-wheeled engines there is only one knuckle joint on each side of the engine ; sometimes it is placed in the rear of the main pin, as shown MODERN LOCOMOTIVE CONSTRUCTION. in Fig. 437 (Art. 309), and occasionally we find it placed in front of the main pin ; there is an advantage in placing it in the rear (see Art. 309). In all consolidation engines one knuckle joint is placed in the rear of the main pin and another one in front of the side-rod pin B (Fig. 488), or in general they are placed in the rear of and ---4- i i JUg. 400 I close to the pins in the third pair of drivers ; and in the front of and close to the pins in the second pair of drivers. The solid ends b I (Fig. 490) of the knuckle joints are generally forged to the central side-rod straps, and the forked ends are forged to the front and rear side-rods. The center lines of the side-rods always lie in one vertical plane, represented by the line C d in Fig. 488. This plane is also represented by the line c d in Fig. 490. In this figure it will be noticed that the center line b b of the knuckle joint does not coin- cide with the center line c d of the side-rods; the reason for this is, that in a great number of engines the inner face /of the flange of the main-rod brass is close to the 340 MODERN LOCOMOTIVE CONSTRUCTION. outer face of the hub of wheel, consequently the inner face e of the knuckle joint must not project beyond the face/ and therefore the center b b of the forked end will often be out of line with center c d of the rod. 348. The form of the pin through the knuckle joint is plainly shown in Fig. 490. A larger portion of its head h is made conical, and the remainder, g, cylindrical ; the diameter of this cylindrical portion is generally a little greater than the diameter of the body of the pin, so that the latter can be passed easily through the hole bored for the head. Another form of the knuckle-joint pin is shown in Fig. 491 ; here the holes in both wings a a 2 of the forked end are reamed out with one tapered reamer ; this plan seems to be the most popular one. The ratio between the length and the diameter of the pin, as made by different builders, varies somewhat, as will be seen by referring to Figs. 490 and 491 ; but we believe good results will be obtained by making the diameter 25 per cent, greater than the length of the pin. Generally, the pins in the knuckle joints are made of wrought-iron, and are case hardened. Iron is to be preferred to steel, as iron pins, particularly when their form is like that shown in Fig. 491, are not as liable to break off in the shank as steel ones. In many engines these pins work in wrought-iron bushings case hardened ; in a few instances they work in brass bearings, arranged as shown in Figs. 441, 445. The knuckle-joint pins should be prevented from turning in their outer bearings ; for this purpose dowel pins are inserted, as shown at p, Fig. 491. So long as the side-rods remain in perfect alignment, the knuckle-joint pins do not rotate in their middle bearings ; under other conditions the amount of rotation is Fig. 491 \e TJ-dia. 1 L H "IT very small. Hence their liability of heating is not so great as that of the crank-pins ; consequently, the pressure per square inch of projected area of a knuckle-joint pin can be considerably greater than the pressure per square inch of projected area of a crank- pin. Careful observation seems to indicate that the projected area of a knuckle-joint pin may be at once determined from the pressure on the piston, and that for every 7,000 pounds of the maximum steam pressure on the piston one square inch of projected area should be allowed. Hence, for obtaining the length and diameter of a knuckle-joint pin, we have the following rules : RULE 84. Divide the total maximum steam pressure on the piston by 7,000 ; the quotient will be the number of square inches in the projected area of the pin. MODERN LOCOMOTIVE CONSTRUCTION. 341 RULE 85. To find the length and diameter of the knuckle-joint pin, divide the projected area, as found by Eule 84, by 5, multiply the quotient by 4, and extract the square root of the product; the result will be the length of the pin. Multiply the length by 1.25 ; the product will be the diameter of the pin. Only fractions divisible by -fa inch are adopted ; hence, if the dimensions found by calculation contain frac- tious not divisible by -fa inch, adopt the nearest one which can be so divided. EXAMPLE 115. It is required to find the dimensions of a knuckle-joint pin for a consolidation engine having cylinders 20 inches diameter ; maximum steam pressure on the piston, 140 pounds per square inch. The maximum pressure on the piston will be 314.16 x 140 = 43982.4 pounds. According to Rule 84, we have 43982.4 = 6.283+ square inches in the projected area. According to Rule 85, we have 6.283 x 4 = 5.02+. The square root of 5.02 is V5.02 = 2.24 inches, which is the length of the pin. And the diameter will be 2.24 x 1.25 = 2.80 inches. Adopting the nearest fractions which are divisible by ^ inch, we have for the length 2 J inches, and for the diameter, 2J inches. By the term " length," we mean only that portion of the pin which is covered by the bushing, or the brass bearing, in which it works. An increase in the steam pressure of 10 pounds per square inch of piston will only slightly increase the dimensions of the pins ; hence, in the following tables we have given one set of dimensions, suitable for steam pressures varying from 120 to 140 pounds per square inch of piston, and another set for steam pressures varying from 140 to 160 pounds per square inch. TABLE 57. DIMENSIONS OP KNUCKLE-JOINT PINS FOR MOGUL, TEN-WHEELED, AND CONSOLIDATION ENGINES, SUIT- ABLE FOR MAXIMUM STEAM PRESSURES ON PISTONS VARYING FROM 120 TO 140 POUNDS PER SQUARE INCH. Diameter of Cylinders. Diameter of Pins. Length of Pint. 11 H inches. 1^ ilK-llfH. 12 li li 13 li 1ft 14 2 1 ," 15 24 Hi 16 2i li 17 2f li 18 J. 2 l!i 2| 24 20 2i 2* 21 3 2f 22 34 i 342 MODERN LOCOMOTIVE CONSTRUCTION. TABLE 58. DIMENSIONS OF KNUCKLE-JOINT PINS FOB MOGUL, TEN-WHEELED, AND CONSOLIDATION ENGINES, SUIT- ABLE FOB MAXIMUM STEAM PBESSUBES ON PISTONS VARYING FBOM 140 TO 160 POUNDS PEE SQUABE INCH. Diameter of Cylinders. Diameter of Pins. Length of Pins. 11 If inches. IT*,; inches. 12 U 1ft 13 14 15 2 2* 2* 1 ,'',; 1 16 2f 1{ 17 if 2 18 2$ 2i 19 3 2J 20 3 2| 21 3i 2* 22 3i 2f CHAPTER VIII. THROTTLE PIPES. THROTTLE VALVE GEAR. SAFETY VALVES. WHISTLE. PUMPS. CHECK VALVES. THROTTLE VALVES. 349. Throttle valves are occasionally placed in the smoke-box, close to the front flue sheet ; when placed there, the throttle valve is simply a plain slide, arranged so as to open or close rectangular ports, which lead the steam into the steam pipes ; but the general practice is to place the throttle valve inside of the dome ; and for such cases a double poppet valve is used. The design of this valve, and that of the throttle pipe, is shown in Figs. 492 and 493. The throttle valve consists of two disks, E E, cast to three or four wings, F F. The upper portion of each one of these disks is generally bounded by a cylindrical surface, and the lower portion, by a conical surface ; the conical portions of the disks fit into seats of corresponding form in the throttle pipe. The angle formed by an element of this conical surface and the axis of the valve is often equal to 45 degrees, but sometimes it is less, as shown in our illustrations. Necessity demands a greater diameter for the upper disk than for that of the lower one, so as to enable us to pass the lower valve through the upper opening. A difference in the diameters of these disks is in nowise objectionable; in fact, it is desirable and advantageous for the following reason : the throttle pipe is surrounded by the steam in the boiler, and when the valve is closed a greater pressure will be on the upper disk than on the lower one, because the former exposes a larger area to the steam pressure than the latter. Under these conditions the valve has a tendency to remain closed when steam is shut off, which is of great importance, as this reduces the liability of engines running away, thus sometimes avoiding serious accidents. The throttle valve is placed in a vertical position, and as high in the dome as possible, leaving between it and the dome-cover sufficient room only for raising the valve so as to obtain around it the necessary amount of opening for the admission of steam. The vertical distance through which the valve must be raised rarely exceeds 1 J inches ; often it is less. The valve is made to fit the valve-stem G quite easy, so as to give the valve ample freedom to come in contact with its seat throughout. The stem G connects to the bell crank /?, and the latter connects to the valve-rod H, which passes through the end of the boiler and connects to the throttle lever. The valve-stem G is always made of wrought-iron ; the bell crank B is sometimes made of cast-iron, frequently of wrought-iron. The valve-rod -fiTis usually a plain, round wrought-irou bar, with brass, cast- or wrought-iron ends I screwed on to it. 344 MODERN LOCOMOTIVE CONSTRUCTION. The throttle pipe, sometimes called the stand pipe, is occasionally made in two pieces, P and (7, as shown in Fig. 493 ; and in many engines it is made in one piece. When made in two pieces, the joint between the flanges M M should be a ground one. This design of throttle pipe (that is, one made in two pieces) is generally used for a dome, having a portion of its top riveted to the dome sheet, leaving a comparatively small opening for a man to enter the dome for the purpose of making the connections When Throttle-valve i*\ cloned the lever B < hould j- touch the projection A, \ on Standpipe C; Then VII .11 II III! Ill I" W| I II' II the Valve must have Vis play at />. between the throttle and dry pipes, that between the bell crank and throttle rod, and others. In a dome with a small opening at top these connections cannot be con- veniently made, and in some cases it is impossible to make them, with the throttle valve in position ; hence the pipe is made in two pieces, so that everything can be properly and securely connected, before the upper portion P, containing the throttle valve, is placed in position. For domes whose whole top can be removed, throttle MODERN LOCOMOTIVE CONSTRUCTION. 345 pipes made in one piece are suitable. Throttle pipes are always made of cast-iron, and therefore the throttle valves should also be made of the same nietal, so as to obtain an equal rate of expansion in the valve and the pipe, thereby preventing leakage. It is on account of the difference in the rate of expansion of the different metals that brass valves in cast-iron pipes have proved to be a failure. Even cast-iron valves will expand lengthways a trifle more than the pipe, and this fact should not be overlooked in fitting the valve to its seat. In order to obtain a steam-tight joint, the valve is ground on its seats, until a perfect fit between both the tipper and lower disks and their 3 Wtngt (thick Fig. 49C T DJ u , * 3 Wtngi i thick Fig., 407 14ft of Valve t Fly. 494 Fig.,498 Fig. 499 seats has been obtained ; the emery should then be wiped off the upper disk and its seat, and a few extra turns given to the valves, so as to very slightly ease the fit between its lower disk and seat ; fitting the valve in this manner will generally secure a steam-tight throttle when the engine is under steam. 350. Figs. 494, 495 represent another design of throttle pipe; Fig. 496 repre- sents the valve. The principal difference between the throttle pipe shown in Fig. 493 and the one shown here is that the latter has at the top a seat A for a snmll relief valve, which is shown in Fig. 497. The object of this relief valve is to prevent 346 MODERN LOCOMOTIVE CONSTRUCTION. the dry pipe N N (Fig. 500) from bursting, which, without this valve, is liable to occur when the engine is suddenly reversed. Springs are not used for holding this valve on its seat ; the steam pressure in the boiler is sufficient to do so. When the valve does lift, it is prevented from lifting too high by the small wrought-iron plate B, held in position by the two studs C C. The elbow, Figs. 498, 499, is bolted to the throttle pipe ; the joint E is a ground joint. The dry pipe N N is made of wrought-iron ; the thickness varies for different sizes of pipes from 7^ to f$ inch ; the former thickness is suitable for pipes 4 inches outside diameter. But dry pipes of the same diameter will not always have the same thickness, as master-mechanics will increase it to suit the steam pressure in the boiler ; the thickness is also frequently increased for pipes longer than the average length of pipes. Dry pipes 1 inches outside diameter are the largest that we have seen used. We believe that for this size of pipe a thickness of -fg inch is sufficient for the greatest length required in any locomotive. The smallest outside diameter of a dry pipe that we have seen used is 4 inches; the diameter for the next size is 4 \ inches ; diameters larger than 5 inches increase by 1 inch. Dry pipes, like boiler tubes, are designated by their outside diameter. 351. A sleeve, generally made of brass, is attached to each end of the dry pipe. In some cases the dry pipe is slipped over the sleeves, but frequently the sleeves / and J are slipped over the dry pipe, as shown in Fig. 500. When the diameter determined by the rule which we shall presently give agrees Fig- BOO with one of the standard diameters of pipes, the best practice is to put the dry pipe inside of the sleeves. Some master-mechanics shrink the sleeves on to the pipe; others fasten them with rivets, generally f inch diameter. Two rows of rivets, from l to 2 inches apart, are used. The pitch of rivets is generally from 2 to 3 inches. The rivets are arranged zigzag ; in some instances twice as many rivets in one row as in the other are used, as shown in Fig. 500. Frequently, instead of using rivets, the holes through MODERN LOCOMOTim CONSTRUCTION. 347 the sleeve and dry pipe are tapped, threaded plugs screwed in, and their ends slightly riveted over, to prevent them from turning and falling out. In our opinion, the best practice is to use iron rivets or plugs ; copper rivets should be avoided, as the action of some kinds of water will produce corrosion between the iron and copper, and con- sequently cause leakage. When the sleeves are placed on the outside of the pipe, and fastened with rivets or plugs, as mentioned, they are calked ; or if the shape of the sleeve will allow it, the ends of the pipe are calked. Pipes placed on the outside of the sleeves always have their ends calked, but sleeves shrunk on the pipe are frequently not calked. Sometimes the ends of the pipe are threaded, and the sleeves screwed on ; in such cases, calking will be a detriment. 352. The end G of the sleeve I (Fig. 500) is turned to a spherical form, and the elbow at F (Fig. 498) is counterbored to a similar shape, so as to make a ball joint between Tig. B01 Wrought Iron e -jtf 4, ^ -] > 1 '' kid i ^ in y + the two. For connecting the diy pipe to the elbow, the yoke shown in Figs. 501, 502, 503 is slipped over the sleeve /and the elbow F; the lugs Y Y are made to bear against the flat end of the sleeve, the point K of the set screw is inserted in the countersunk cavity L in the lug M (Fig. 498), and the sleeve I drawn tightly against spherical face F, and fii'mly held there. Although this mode of fastening the dry pipe to throttle pipe is often used, and gives good satisfaction, other designs for accomplishing the same thing are adopted ; for instance, for a throttle pipe like that shown in Fig. 493, two hooked bolts instead of a yoke are used. But in all cases the joint between the throttle pipe and dry pipe is a ball joint, which affords ready means for adjusting the dry pipe to any inaccuracies which cannot be avoided in the construction of a boiler. The sleeve J at the other end of the dry pipe (Fig. 500) is also made so as to form a ball joint, with a casting riveted to the front flue sheet ; this casting or ring will be presently shown. 353. Figs. 504, 505 represent another throttle pipe, and Figs. 506, 507, 508 show some of its details. The design of this throttle pipe does not differ much from those previously shown. The principal differences ai-e that the pipe is made in one piece, and that the sleeve 7 is of a different form. The manner of fastening the 348 MODERN LOCOMOTIVE CONSTRUCTION. dry pipe to the throttle pipe is plainly shown, and does not need any further explanation. The favorite way of fastening the throttle pipe to the dome is plainly shown in 4) p ^ V 7) Flg.i i ' p_ 1 i i _._ -.- r 1 -* ! F J w aW/ttWWy " [f 1 ; - ijj r' 1 i i V 'H f I ^! fl'f .. 5 -- j -: ! 3^ ! ^"~* c-i-4- -[4 -ii *- i i , m [ f 1 A" ! I ! if sffi *I * ^^ r i i a, y. f f f Jlij/:. S04 r these figures. A bracket D is cast to the throttle pipe, and fastened to the dome sheet F by two studs. When possible, all dry pipes are allowed to rest on top of the crown MODERN LOCOMOTIVE CONSTRUCTION. 349 bars. When this cannot be done, the dry pipe is suspended by a strap, usually made of - J x i-inch iron, bolted to the boiler shell W. The thickness of the throttle pipes is generally about to f inch. Fig. 504 represents a pipe exceptionally thin, the thickness being only -fa of an inch ; and for this reason the thickness at the lower end is increased, so as not to injure it in clamping the dry pipe to it. The inner diameter of the throttle pipe is generally made proportionate to the diameter of the cylinder ; the ratio between the two, as made by different builders, varies. Hence we sometimes find the inner diameter of the throttle pipe equal to one- quarter of the diameter of the cylinder, and frequently we find it to be equal to about one-third of the diameter of the cylinder. The latter we believe to be the best propor- tion, and should be adopted. When the inner diameter of the throttle pipe is not uniform throughout for instance, if the throttle pipe is made similar to that shown in Fig. 504 the smaller diameter P should be one-third of the diameter of the cylinder. The inner diameter of a throttle pipe should not be greater, in any case, than here given. If made much smaller, so that the cross-sectional area of the throttle pipe is less than one-tenth of the cross-sectional area of the cylinder, the initial steam pressure in the cylinder at high speeds will be reduced below the boiler pressure more than it would be otherwise, and the tractive power of the engine will be interfered with. On the other hand, practice seems to indicate that no advantage is gained by making the inner diameter of the throttle pipe greater than one-third of the diameter of the cylinder ; in fact, throttle pipes and diy pipes too large in diameter are detriments to the engines, because an unnecessary quantity of steam held in these pipes must be worked off before the engine can be stopped, which is an objection in case of an emergency. The cross-sectional area at 0, Fig. 504, is generally rectangular in form ; the length and breadth of this section should be so proportioned as to give an area equal to that through the cylindrical portion of the pipe. 354. The inner diameter of the dry pipe should be equal to that of the throttle pipe; but since in many cases the diameter of the pipe, determined by calculation, cannot be found among the standard diameters of dry pipes, the next larger size is adopted ; and therefore we often find locomotives having dry pipes whose inner diame- ters are greater than those of the throttle pipes. The outer diameter of the upper disk of the throttle valve is sometimes a little greater than the inner diameter of the throttle pipe ; frequently it is less. A good rule is to make the outer diameter of the upper disk equal to one-third of the diameter of the cylinder. The outer diameter of the lower disk is made from to of an inch less than the diameter of the upper opening in the valve seat. 355. Fig. 510 represents a complete sectional view of the connections of the T-pipe and dry pipe N. The brass ring B z is riveted to the flue sheet A ; another view of this ring is shown in Fig. 509. The six holes marked s s in Fig. 509 are tapped for the studs marked F F in Fig. 510 ; the remaining holes r r are the rivet holes. The size of rivets and studs vary according to the size of engine ; for small engines, say with cylinders 10 inches diameter, the rivets through the ring 11., are generally f inch diameter, and the studs f inch diameter ; for engines with cylinders 350 MODERN LOCOMOTIVE CONSTRUCTION. 20 inches diameter, rivets 3 inch di- ameter and studs 1 inch diameter are generally used. The flue sheet A is bored out to receive the projection on the brass ring B 2 . The spherical seat in this ring is made to fit the spherical surface on the sleeve J\ this sleeve, we have seen in Art. 351, is riveted to the dry pipe 2V. The T-pipe has a spherical projection p, bearing against the surface of the counterbore in the sleeve J ; some builders make this couuterbore a conical surface; others make it a spherical surface as shown ; but in all cases, the projection p on the the T-pipe is turned to a spherical form. The diameter of the opening M in the brass ring must be made suffi- ciently large to admit the sleeve on the other end of the dry pipe; this condition will determine to a great ex- tent the size of the ball joint on the sleeve J. It will be seen that the studs F F force the T-pipe against the sleeve J, and the latter is, in turn, pressed against the ring B 2 , thus form- ing steam-tight joints between the whole. Some builders do not use a brass ring B 2 for small locomotives, but use in place of it a wrought-iron plate P P, as shown in Fig. 512. In fact, some master-mechanics prefer the wrought- iron plate P P for all sizes of engines, and consequently we frequently meet with large engines which have a plate of this kind in place of the brass ring. The plate is riveted to the flue sheet A A ; the arrangement of rivets and studs for holding the T-pipe is similar to that in the brass ring as shown in Pig. 509. Both the flue sheet and the plate are then couuterbored as shown, so as to form a bearing for the spher- ical part of the sleeve J. MOVER* LOCOMOTIVE CONSTRUCTION. 351 356. The right-hand side of Fig. 511 represents an outside view of the T-pipe, and the left-hand side represents a section of the connection of the T-pipe and the steam pipe 1). The steam pipes lead to the cylinders. A complete drawing of these pipes and their position in the smoke-box will be found in Fig. 24. In fact the .illustrations here given simply show in detail and to a larger scale the connections of the dry pipe, T-pipe, and steam pipes. The opening in the flanges E E of the T-pipe are counterbored to a spherical form for the brass rings C, which are inserted between the T-pipe and steam pipes. Usually two bolts G G are used for connecting each steam pipe to the T-pipe. The inside diameter K of the T-pipe must be equal to that of the throttle pipe. The area of the opening L in the branches of the T-pipe should be equal to the inner cross-sectional area of the stearn pipe. The rale for finding this area has been given in Art. 46. 357. Fig. 511A shows a throttle pipe arranged to take a device for furnishing dry steam to the cylinders. This is accomplished by separating the steam from the water Fig. 5 11 A when the engine is running. The device is called a separator, and consists of a single casting with the necessary drain pipes for leading off the water after it has been separated from the steam. It will presently be seen that its construction is exceedingly simple ; it is very durable, and requires veiy little or no attention. The separator is cast in one piece. Its core B is made hollow, and is gradually reduced from a comparatively large diameter at the center to a point at each end, so as to form a conoidal surface. A number of wings C C are cast to this surface and 352 MODERN LOCOMOTIVE CONSTRUCTION. extend spirally towards the ends of the core. This separator is set concentric with the throttle pipe, whose diameter is necessarily somewhat larger than that of an ordinary one. The separator does not rotate, but it is firmly attached to the pipe as shown. In Fig. 511B it will be noticed that one side of each wing is formed tangential to the surface of the core, and the other side approaches a radial surface. The object of the whole construction is to divide the steam as it flows through the pipe into several smaller currents, and to give to each a compound whirling motion which is accomplished in the following manner. The core B of the separator spreads the steam or, so to speak, expands it into an annular body, and the wings C C divide it into several streams or currents, while their spiral forms impart to each current a whirling motion around the core ; and the sides tangential to the surface of the core impart to each stream a whirling motion within itself. It will also be noticed that by expanding the steam into an annular body and cutting it up into several streams all the suspended particles of water will be affected by the whirling motion. If, on the other hand, the solid stream as it enters the separator had not been expanded into an annular body, the whirling motion could not act on the particles of water in the center, and the action of the separator would thereby be impaired. The result of all this is that as the steam enters the throttle pipe a violent, compound whirling motion is imparted to all the particles of steam and water, all the heavier particles are thrown against the pipe, and the water thus separated from the steam flows into the annular chamber at the bottom of the throttle pipe, whence it is con- ducted through the tube J to the outside of the boiler and may be fed back to it if desirable. The dry steam is conducted through the vertical branch H into the dry pipe leading to the cylinders. The bell-shaped cup G gathers any water which may flow along the core B, which is discharged into the tube 7, which carries it off with the rest of the water. In applying this separator to a locomotive nothing needs to be changed excepting the throttle pipe. There is nothing to get out of order, which is an important feature in mechanical devices which are placed out of sight and cannot be reached like a throttle pipe in a locomotive boiler. This separator is the invention of Mr. Joseph De Rycke of New York. It has been successfully used in many marine engines and on steam mains from 200 to 800 feet in length ; but we are not aware that it has yet been applied to locomotives, for which we believe it is well adapted. THROTTLE VALVE CONNECTIONS. 358. There are various ways of attaching the throttle valve connections to the boiler. Sometimes we are compelled to run the throttle lever connections through the top of the boiler ; but generally the throttle rod passes either through the back head of the boiler, or it passes through the sides of the dome. Figs. 513, 514, 515 repre- sent a throttle valve lever and its attachment, suitable for engines in which the throttle rod H is passed through the back head of the boiler. The throttle lever is probably the simplest in design used on locomotives. The back head P P of the boiler is bored out to receive the spherical portion of the stuffing- MODERN LOCOMOTIVE CONSTRUCTION. 353 box C, the two forming a ball joint ; this joint is a ground one, so as to make it perfectly steam tight. The stuffing-box is fastened to the boiler head by four studs, .L, M, K, K; the studs K, K are made long enough to take hold of the stuffing-box gland. The form of the nut on the stud M is made suitable for receiving a pin, on which the two links 0, vibrate. These links are connected to the throttle lever A, and act as a fulcrum. The throttle lever A is connected to the throttle rod H by means of the jaw 7. In a few instances this jaw is screwed on to the rod H, but generally the jaw is bored out to a taper, accurately fitting the tapered end of the rod H, which is driven into the jaw, and held there by means of the tapered pins G, G ; in some cases only one pin in place of two is used. The taper on the end of the rod H is generally inch in 2 inches. The throttle lever rests on the quadrant B, which is fastened to the boiler head by means of one stud; in a few instances two studs are used for the same purpose. Through the quadrant B, a slot is cut for the clamping bolt F; the nut E for this bolt is capped with wood. The throttle lever A is clamped to the quadrant B in any position which gives the throttle valve in the dome the desired degree of opening. This design of lever is often adopted on account of its simplicity ; but it is not a convenient one for the engineer to handle, because in order to open, close, or adjust the throttle valve with this kind of lever the engineer may have to use both hands, which is not only inconvenient, but in case of an emergency is objectionable. 354 MODERN LOCOMOTIVE CONSTRUCTION. 359. Figs. 516, 517 represent a throttle lever and attachments designed to remove the objectionable feature inherent in the former one. The principal difference between the two designs lies in the de- sign of the quadrant B. In Fig. 516 it will be seen that on the convex edge of the quadrant B notches are cut which engage with corresponding teeth on the end of the latch S; this latch is connected to the handle B by the link T. It will readily be perceived that, with this arrangement, the engineer can /k ' f t -v ' ( i- H :i ' i ' -J, ! ! ' 1 f l-ll '- 1 ! i; - i! r UJ with one hand disengage the latch, move the lever into any position, and allow it to lock itself there. The manner of fastening the quadrant B (Fig. 516) to the boiler differs somewhat from that shown in Fig. 514, In the former figure it will be noticed that a bracket -B 2 MODERN LOCOMOTIVE CONSTRUCTION. 355 is fastened to the boiler, and the quadrant B is attached to this bracket. In many engines the bolt U does not hold the quadrant B i-igidly to the bracket, but allows it to vibrate a little, so as to adjust itself to any position of the lever A. Under these conditions, we need in the quadrant B a slot cut equidistant from the notched edge of the arc. In this slot a bolt F is accurately fitted, and prevents a disengagement of the quadrant B and the latch S. These are usually placed above the lever ; in such cases, the bolt F will tend to prevent the lever from moving out of its appointed plane of action, and help to produce steadiness of motion. 360. The diameter of the throttle rod H varies for the different sizes of engines ; for small engines it is about J inch, and for large engines about Ij inches. To place the throttle rod H in position, it must be passed through the stuffing- box; hence, collars on the i-od are not admissible. When these rods are made of uniform diameter throughout, they must be turned throughout their whole length ; to save time in turning, a largo portion of the rod, extending to within a short distance from the ends, is forged about j- 6 of an inch smaller in diameter than the required finished diameter at the ends, leaving at the throttle-lever end a portion to be finished, of a length only as may be required for the movement of the rod in the stuffing- box, and leaving at the throttle-pipe end a portion of such a length as may be required for the thread. Sometimes that part of the rod which works in the stuffing-box is provided with a brass casing, as shown in Fig. 516. This brass casing is cast on the rod ; its object is to prevent a collection of rust between the rod and stuffing-box. The portion of the rod covered by the brass casing is generally forged to an octagon form. 361. The stuffing-box is generally made of cast-iron, sometimes of brass. For large engines the stuffing-box gland is often made of cast-iron. Glands made of cast- iron have always a brass bushing. The bushing is sometimes driven into the gland with a hammer, and sometimes it is pressed in by a hydraulic press with a pressure of about 100 pounds. For small engines, the gland is often made of brass. The principal propor- tions of the gland and stuffing-box are found by the rule given in Arts. 192, 193, 194, and 195. 362. The quadrants B, having a form similar to that shown in Fig. 514, are made of brass, and when they are made like that shown in Fig. 516 they should be made of the best hammered iron or steel, so as to prevent wear of the notches. The shape of the notches is similar to that of the teeth in an ordinary circular saw ; the notches are cut so as to bring their radial sides towards the boiler. Notches of this kind will prevent the throttle valve from flying open, and allow it to be veiy easily closed. 363. Sometimes the throttle lever A is placed in a horizontal position ; in many engines it points upward, and occasionally it points downward. The proper position of the throttle lever will depend on the position of the stuffing-box in the back head, and the position of the reverse lever. The stuffing-box is placed as high in the back head as is possible and practical to do, and determines the position of that part of the throttle lever which is connected to tin' throttle rod. The handle of the throttle lever should be as close as possible to the handle of the reverse lever, the latter being placed in a convenient position for the 356 MODERN LOCOMOTIVE CONSTRUCTION. engineer to reach; hence in this way the position of the end of the throttle lever is found, and the plane in which it is to move is established. The distance between the extremity of the throttle-lever handle and that of the reverse lever should be about 2j to 3 inches, so as to prevent the engineer from jamming his hand between the two ; hence this condition will determine the length of that part of the throttle lever which extends from the center of the throttle rod to the extremity of the handle. 364. The objection raised to the throttle lever shown in Figs. 516, 517 is that the pitch of the teeth on the quadrant B will limit the degree of opening of the throttle valve, 4 and in some cases will not be as close to the requirements of the engine as may be desirable. Again, on account of the fine pitch of the teeth in the quadrant 7?, strength, and consequently security, will be impaired ; and also in some cases the wear of the teeth is objectionable. Figs. 518, 519 represent a throttle-valve lever designed to overcome these objec- tions. In this arrangement a curved rack B instead of a quadrant is introduced ; the rack is placed under the lever A. This rack engages with a small pinion C keyed to the stud D ; to the same stud is keyed another wheel E, larger in diameter than the pinion ; the wheel E is an internal-spur wheel, whose teeth engage with the link T, preventing the stud D from turning, and thus locks the throttle lever in the desired position. The reason for placing the teeth inside of the wheel E is simply to obtain a pleasing effect, exposing to view plain and polished surfaces, which can be kept clean. The MODERX LOCOMOTIVE CONSTRUCTION. 357 link T is connected to the handle E, the spring S holds the link T in contact with the teeth in the wheel E. In pressing the handle R towards the throttle-lever handle, a disengagement of the link T and the wheel E takes place, enabling the engineer to move the throttle lever to and fro with ease. In this aiTangernent the wear of the teeth in the rack will be less than the wear of the teeth in the quadrant shown in Fig. 516 ; also, because the pitch of the teeth in the rack and in the wheel E is greater than the pitch of the teeth in the quadrant B (Fig. 516), the strength of this arrangement, and security, is increased. A very close adjustment of the throttle valve to the requirements of the engine can also be obtained ; indeed, this closeness of adjustment largely depends upon the difference between the diame- ters of the wheel E and the pinion C. For instance, suppose that the pinion C makes just one complete turn in lifting the throttle valve one inch, then the wheel E must of course also make one complete turn during the same time ; if now the wheel E has 42 teeth, then it must be obvious that the throttle valve can be set to -fa inch ; and if a closer regulation is required without changing the pitch of the teeth in the wheel E, then we have only to increase its diameter so as to enable us to increase the number of teeth. 365. The method for finding the length and curvature of the pitch line for the rack B is the same as that for finding the length and curvature of the quadrants B in Figs. 514 and 516. In order to explain this method, we have shown in Fig. 524 a portion of the throttle lever A, the links 0, and a portion of the quadrant B. Before we can determine the length and curvature of the quadrant we must know the lift of the throttle valve ; hence the following problems present themselves : first, to find the lift of the throttle valve ; second, to find the length of the arc c n d ; third, to find the radius of the same arc. 358 MODERN LOCOMOTIVE CONSTRUCTION. First, to find the lift of the throttle valve. To explain this, we shall refer to Fig. 504. In this figure we see that the smallest inner diameter (4f inches) of the throttle pipe is at the bottom of the pipe ; the area of a circle 4| inches diameter is 16.80 square inches ; hence the throttle valve must have a lift which will allow such a quantity of steam to enter as can pass through an area of 16.80 square inches. Again, we see that the valve seats are of a conical form ; but, for the sake of simplicity in finding the lift, the valve seats are assumed to be flat. Under these conditions the lift of the valve must be such that, when the circumferences of the inner edges of the valve seats are multiplied by the lift, the area thus obtained will be equal to the smallest inner cross- sectional area of the pipe, which in our case is 16.80 squai'e inches. In Fig. 504 we see that the diameter of the inner edge of the upper throttle-valve seat is 4 inches, hence its circumference will be 4.5 x 3.1416 = 14.13+ inches; the diameter of the inner edge of the lower valve seat is 4 inches, its circumference will be 4 x 3.1416 = 12.56+ inches ; the sum of the two circumferences will be 14.13 + 12.56 = 26.69 inches; hence in the case before us the lift will be K-T^ = .62+ inch. But .iO.uy this lift is suitable only for flat valve seats, and will not give us a sufficient opening for conical valves. In nearly all locomotives the inclination of the valve seat varies but little from an angle of 45 degrees from the axis, and therefore we will generally obtain good results by adding 50 per cent, to the lift just found ; hence the lift for the valve shown in Fig. 504 should be .62 + .31 = .93 inch. From the foregoing we may establish the following rule : RULE 86. Divide the smallest cross-sectional area of the throttle pipe by the sum of the circumferences of the openings in the valve seats ; add 50 per cent, to the quotient ; the sum will be the lift of the valve. If now the lengths of the arms of the bell crank to which the valve-stem and throttle rods are connected had been equal, the throttle rod H would have to move through a distance of .93 inch. But in Fig. 504 we see that the arm of the bell crank to which the valve-stem connects is 2 inches long, and the other arm is 9 inches 9 long, hence the movement of the throttle rod will be ~ = 3.6 times greater than the ay lift of the valve ; and if the lift of the valve is .93 inch, then the total movement of the throttle rod will be 3.6 x .93 = 3.348 inches, say 3f inches. Second, to find the length of the arc c d, Fig. 524. To make the solution of our problem as plain as possible, let us assume that Fig. 524 is a portion of the throttle work, as shown in Fig. 514. Draw the center line k I of the throttle rod H, and on it lay off two points, k and / ; the distance between these points must be equal to the travel or movement of the throttle rod ; if this travel is to be 3f inches, as found by the foregoing calculations, then make the distance between k and I equal to 3f inches. When the throttle- valve is one-half open, or, in other words, when it stands in the center of its lift, the center line p t of the throttle lever A stands generally parallel to the back end of the boiler and the center line e/of the link stands perpendicular to p t, as shown in Fig. 514. Under these conditions, draw through the center m (Fig. 524) of the movement k I a t perpendicular to k /, and a line cf perpendicular to p t, cutting the latter in the MODERN LOCOMOTIVE CONSTRUCTION. 359 point/; the distance between the lines k I and ef must of course be equal to the given distance between the center line of the link and the center line of the throttle rod ; in Fig. 514 we see that this distance is 3 inches. The point /will be the center of the fulcrum pin through the end of the lever A, and the point m will be the center of the pin through the lever A and the throttle rod H. On the line p t lay off a point n, and make the distance between m and n equal to the given distance between the center of the pin m and the center of the clamping bolt ; in Fig. 513 we see that this distance is 6 inches. Now, the center e in the link will be stationary, the center /will move along the arc g It described from the center e, and the center m will move along the straight line A; /. Therefore from the point A; as a center, and with a radius equal to the distance between / and m, describe a short arc cutting the arc g h in the point i, join the points i and A; by a straight line, and prolong it towards r. Again, from the point / as a center, and with a radius equal to fm, describe a short arc cutting the arc g h ; the point in which these two arcs intersect will very nearly coincide with the point i, previously found ; for all practical purposes we may assume that these points coincide. Through the points i and I draw a straight line, and prolong it towards s. Make k r equal to m n ; also make I s equal to m n. When the throttle valve is closed, the center line of the throttle lever A will coincide with the line i r, and the point r will be the position of the center of the clamping bolt. When the throttle valve is full open, the center line of the throttle lever A will coincide with the line i s, and the point s will be the position of the center of the clamping bolt. The arc r n s will represent the length of the path of the center of the clamping bolt. In practice it is customary to make the arc r n s about 1 inch longer than length just found, consequently the length of the arc end will be equal to the sum of the arc r n s, as found by construction, plus the diameter of the clamping bolt, plus 1 inch. Third, to find the radius of the arc end. This arc will not coincide exactly with an arc of a circle, yet the difference is so slight that it may be neglected, and for all practical purposes we may assume that the arc c n d is an arc of a circle. Now, the points r n s are points in this arc, hence all that is necessary is to find a point p, from which an arc can be described which will pass through the three points r n s; the distance from p to any one of these points will, of course, be the required radius. Probably the quickest way to find the point p is by trial ; it can also be found in a geometrical way, by joining the points r and n by a straight line ; also joining the points n and s by a straight line. Then bisect the lines r n and n s by perpendicular lines; the point in which these perpendiculars intersect will be the center _p from which the arc r n s is to be described. The lines u v and iv x extend, and ai-e perpendicular to the back head of the boiler ; the distance between the center line of the throttle rod H and the line u v will depend on the position of rivets in the head of the boiler, and this distance should be so adjusted that the stud or studs whii-li fasten the quadrant B to the boiler will be clear of the rivet heads. 366. The following figures represent a throttle-lever arrangement for engines, in which the throttle rod passes through the side of the dome. Similar letters in the different views indicate the same details. 360 MODERN LOCOMOTIVE CONSTRUCTION. HI ,1 5\ ft t *s \ <-vW 7* k i-< } A ffl Fig. 525 represents this throttle-lever arrangement as seen from the back end of the boiler. Fig. 526 is a plan of the same ; Fig. 527, a section of the steam-gauge stand, stuffing-box, gland, and steam-pipe connecting the steam-gauge stand to the MODERN LOCOMOTIVE CONSTRUCTION. 361 dome ; Fig. 528 shows the throttle rod, and Fig. 529 the link used for connecting the throttle lever to the steam-gauge stand. The steam-gauge stand marked A is often made of cast-iron, sometimes of brass, tl'^,Threadi.fo one. inch., Fig. 527 and is bolted to the top of the boiler by means of two studs pass- ing through the holes a a. The throttle rod G works in the brass stuffing-box B, which is fastened to the steam-gauge stand by means of the two studs b b ; these studs are also used for tightening the brass gland C. The stuffing-box is bored out at one end to receive the hemp packing and the gland ; the other end of the stuffing-box is tapped, and the wrought-iron tube or pipe K screwed into it. This pipe is about ^ of an inch thick, and is the same kind of tubing as used for water grates, to which we shall refer later on. The other end of the pipe K is screwed into a small brass flange ; the latter is riveted to the outside 362 MODERN LOCOMOTIVE CONSTRUCTION. of the dome, and is completely covered by the dome casing. The pipe K is not bored out ; its inner diameter is somewhat larger than the diameter of throttle rod G, so as to give the latter ample freedom for its motion. The purpose of the pipe K is to cover and protect the throttle rod, and in the meantime bring the stuffing-box B and gland C which are required in any case within easy reach of the engineer. In this design the jaw H and the jaw at the opposite end of the throttle rod are keyed to the latter, as indicated in Fig. 528 ; this way of fastening the jaws to the throttle rod differs a little from the manner of fastening similar jaws on rods, as pre- viously illustrated. The wrought-iron link I forms a connection between the throttle lever E and the lug C 2 cast to the steam-gauge stand A, and serves as a fulcrum for the former. The manner of locking the lever E differs greatly from any of the previous de- signs. The upper side of the jaw H (Figs. 525, 526) is extended sideways and formed into a circular rack ; the pitch of the teeth is very fine, so as to obtain a regulation of the lift of the throttle valve as close as possible to the requirements of the engine ; yet with this arrangement it will be difficult, if not impracticable, to obtain as close a regulation as with the design shown in Fig. 518. A steel latch L, having three or four teeth cut in its end, engages with the rack. The lug forged to the bottom of the latch, and sliding in a slot cut through the lever, serves as a guide for the latch ; the link F connects the latch to the handle M, which, in being pressed towards the throttle- lever handle, disengages the latch from the rack, and leaves the lever free to move. In moving the lever to and fro, the latch L will move faster than the pin d, and it is on account of the difference between the rates of these motions that when the latch L engages with the circular rack the lever is locked. The steam-gauge is fastened to the upper part of the stand A ; the center /of this part coincides with the center of the steam-gauge. The handle Z> J9, Figs. 525, 526, is for the purpose of opening one of the safety valves, or regulating the pressure on the same ; the pin li connects a spring balance not shown to the lever D ; this spring balance stands in a vertical position, with its upper end attached to the safety-valve lever; the handle D swings on the pivot i, which is cast on the back of the steam-gauge stand A ; the pawl N engages with the teeth cut on the edge of the steam-gauge stand, and prevents the lever D from moving upwards. In pulling the lever downwards, the pressure on the safety valve will be increased. The safety valves and spring balance will be described later on ; all that we need to say here is that two safety valves are always used for a locomotive boiler, and it is only one of these that can be released, or the pressure upon it changed by the lever D ; the other safety valve is or should be beyond the control of the engineer. Fig. 530 represents a wrought-iron steam-gauge lamp bracket for the throttle valve gear shown in Fig. 525 ; its end p is inserted in the hole g in the lower part of the stand A, and fastened there ; the steam-gauge lamp is screwed on to the end I of the lamp bracket. 367. In this design of throttle-valve gear the pitch line of the teeth in the circular rack must be described from the center d, Fig. 526, and not from a center lying to the left of it for instance, such as we were compelled to find by the construction shown in Fig. 524. MODERN LOCOMOTIVE CONSTRUCTION. 363 For obtaining the length of the circular arc that is, the distance from h to i, Fig. 531 we simply describe from the center d the arc h i, which contains the outer extremities of the teeth, and then proceed as follows : Let the point d, Fig. 531, represent the position of the center of the pin when the throttle valve is closed. Through the point d draw the center line m n of the valve- rod, and on this line mark off a point d% ; the distance between the points d and d 2 must be equal to the distance through which the center d of the pin will travel to open the throttle valve fully ; this distance is found as explained in Art. 365, and is usually about two inches, or a little more ; in some cases it may be as much as 2 inches. Fig. SSI Lay off a point c to represent the center of the lug cast on the steam-gauge stand ; the location of the point c must, of course, correspond relatively to the position of the point d. From the point c as a center, and with a radius equal to the distance between the centers of the holes in the link 7 (Fig. 529), describe a short arc r s ; also from the point d as a center, and with a radius equal to the distance between the centers d and e that is, the given distance between the centers of the holes in the lever E describe an arc t u cutting r s in the point e ; the straight line joining the points c and e will be the center line of the link /. Through the points c and d draw a straight line, and prolong it towards L, cutting the arc h i in the point #. Now the center line e L indicates one of the extreme positions of the throttle lever E (that is, when the throttle valve is 364 MODERN LOCOMOTIVE CONSTRUCTION. closed), and theoretically the arc h i need not extend beyond the edge v of the latch L ; but, in order to allow for wear and inaccuracies in fitting, the distance from g to h is usually such as to extend $ of an inch beyond v ; hence the total distance from g to h measured on the arc h i will be about If inches. Through the point d draw a line d k perpendicular to m n, cutting the arc h i in the point q, and thus obtain the distance Ji q that is, the distance from the point h to the line d k, measured on the arc /* i. If now a line w x, perpendicular to m n, be drawn through the point w that is, the middle of the distance d d 2 and the line w x passes through the point e, as shown, then the motion of the lever E will be symmetrical on each side of the line e w ; under these conditions we have only to make i q equal h q, and thus obtain the whole length of the circular rack Ji i. If the line w x does not pass through the point e, then, the point h having been found as before, the point i 2 will be found in the following manner : Through the point d 2 draw the line d 2 k 2 , perpendicular tomn; also from d 2 as a center, and with a radius equal to d e, describe an arc to cut the arc r s ; in practice the point of intersection thus found will generally be so near to the point e that we may consider the former to coincide with the point e. Through the point e and d 2 draw a straight line, and prolong it towards f 2 . From the point d 2 as a center, and with a radius equal to d g, describe the arc q 2 i 2 , cutting ef> in the point #,, also cutting the horizontal line d 2 k 2 in the point q 2 . Make g 2 i 2 equal to g h, add the arc q 2 i 2 to the arc h q, and thus obtain the whole length of the circular rack. 368. In Art. 366 we have shown a throttle-valve gear attached to the top of boiler, with the throttle rod passing through the side of the dome. Figs. 532, 533, 534 repre- sent another throttle- valve gear, also attached to the top of boiler, but differing from the former in having the throttle rod H pass through the top of the boiler instead of passing through the side of the dome. Fig. 532 represents the relative positions of the steam-gauge stand A, the stuffing- box B with gland C, and the throttle lever E. Fig. 533 simply represents a plan of the stuffing-box and gland, the throttle lever, and the notched quadrant D ; the steam- gauge stand is not shown in this figure. Fig. 534 represents the relative positions longitudinally of the stuffing-box and steam-gauge stand ; and Fig. 535 represents a plan of the latter. The throttle rod If stands in a vertical position. The ends of the throttle rod which pass through the lever E and the crank I are cut square. In Fig. 532 the line d is the center line of the boiler, and since the center line of the throttle pipe in the dome coincides with the line d, and since the center /of the pin through the small crank I should also coincide, or nearly so, with d, it follows that the stuffing-box must be placed on one side the center line d. The joint between the stuffing-box and top of boiler is a ground ball joint ; around it, the thickness of metal is increased by riveting a small plate K to the inside of the boiler, thereby obtaining a sufficient depth of metal for the threads on the studs o, a 2 , a 2 , which fasten the stuffing-box to the boiler ; the studs a 2 a -i are made long enough to take hold of the gland C. -^ a 366 MODERN LOCOMOTIVE CONSTRUCTION. The steam-gauge stand A is fastened to the top of boiler with two studs, b b. The depth e of the steam-gauge stand flange may seem to be excessive ; this depth, as well as the distance from the top of the stuffing-box flange to the top of boiler, will be gov- erned by the following conditions : The. designs of throttle- valve gears shown in Figs. 525 and 532 are generally required for boilers which extend nearly to the rear end of the cab ; the portion of the boiler inside of cab must be lagged, as well as the outer portion, so as to prevent a loss of heat by radiation, and also to prevent the cab from becoming uncomfortably hot for the engineer. The distance between the outer face of lagging and the boiler usually varies from about Ij to 2 inches ; now, in order to make a nice and easy finish of the lagging around the steam-gauge stand and stuffing-box, the upper faces of their flanges are made to extend about \ inch beyond the lagging, hence the excessive depth e of the steam-gauge stand flange and the seemingly unnecessary height of the stuffing- box flange. The quadrant D is bolted to the steam-gauge stand ; this quadrant must, of course, be described from the center of the throttle rod H. It will be noticed that in this design the quadrant D is made to pass through the throttle lever E, instead of being placed below or above it, as shown in some of the other designs of throttle-valve gear. The manner of locking the throttle lever E is so plainly shown in Fig. 533 that an explana- tion is unnecessary. The arc y h i, Fig. 533, represents the path of the end of the throttle lever ; the distance between its extremities g and i is usually about 12 inches, and should not exceed 18 inches. Now, to keep the movement of the end of the throttle lever within these limits, and in the meantime give the throttle valve the required lift, no more and no less, we must assign a suitable length to the crank I in Fig. 532. But in many cases the boiler braces will determine the position of the stuffing-box B, which will also fix the length of the crank 7; the length thus found may not be suitable for keeping the movement of the throttle lever within the given limits ; under these conditions we must give such lengths to the arms of bell crank B, Fig. 493, as will produce the desired results. The given limit of the movement of the throttle lever will also, in many cases, determine the distance between the holes e and d in Fig. 531. 369. We have already seen that the design of the throttle- valve gear shown in Figs. 525, 526 is used on engines whose boilers extend nearly to the rear end of the cab. This class of engines, or the class of engines in which the throttle-rod passes through the side of dome, generally present first-class opportunities for making pro- visions for attaching the various kinds of valves and cocks without screwing each one directly into the boiler shell. Consequently, in many of the locomotives of these classes built in recent years, we find a throttle- valve gear like that shown in Figs. 536, 537, or others, very similar in design to the one here shown. In these illustrations we have only represented the most prominent features of this design of throttle- valve gear ; for the sake of simplicity the throttle lever, with its attachments for locking it, is not shown ; in fact, any one of the throttle levers previously illustrated, with only a slight modification in a few of them, can be used in this kind of gear. Its principal feature is the steam stand B, which is simply a rectangular box, generally made of brass. In Fig. 536 we see a longitudinal section of this box, and Fig. 540 shows a cross- /HW3~T " / ~pj :SJ B' PS" 368 MODERN LOCOMOTIVE CONSTRUCTION. section of the same. These figures plainly indicate that the steam stand B is divided into two compartments or chambers, D and C; the chamber C nearly surrounds the chamber D. Communication between these two chambers is either opened or closed by means of the valve e. The throttle rod H passes through the chamber D, and also through the heavy wrought-iron pipe_EJ; the latter forms a connection between the steam stand B and the dome G. The rear end of the steam stand is bored out so as to form a stuffing-box ; h is the stuffing-box gland. The end i of the throttle rod H is fastened to the throttle jaw (not shown here), and this throttle jaw connects to the throttle lever. The steam-pipe E is connected to the dome by means of a thimble K, which takes the place of a brass flange. A part of the outer portion of this thimble is hexagonal in form, the remaining outer portion is threaded and screwed into the dome sheet. A portion of this thimble is tapped and receives the threaded end of the pipe E. This is a favorite way, in locomotive practice, of connecting a pipe of the kind here shown to the boiler. On the other end of the pipe E a wrought-iron sleeve / is screwed. A separate view of this sleeve is shown in Fig. 543, and, as will be seen, it forms a ball joint with the steam stand ; this sleeve is held against the stand by the flange F, of which a separate view is shown in Fig. 542. Fig. 537 represents a plan of the steam stand B ; here it is plainly seen that its sides have a number of tapped holes; into these the various valves and cocks are screwed, which otherwise would have to be screwed into the shell of the boiler. For instance, the holes a a receive the injector valves ; b b receive the cylinder oil-cups ; c receives the blower valve ; and s the steam-gauge cock ; the hole d on top of the stand takes the brake valve. Steam is conveyed from the dome through the pipe E, and enters the chamber D in the steam stand ; when the valve e is open the steam enters the chamber C, and supplies all the valves attached to the steam stand. Fig. 541 shows the spindle of the valve e on a larger scale ; Fig. 538 shows the front end of the steam stand B, and a portion of the steam-gauge stand A ; Fig. 539 shows the rear end of the stand B, with stuffing-box gland h; the tapped hole g receives the fulcrum for the throttle lever. In Fig. 536, 8 is the steam-gauge, and L the steam-gauge lamp. We believe this arrangement to be one of the best and neatest in use. All the holes in the steam stand B can, of course, be drilled in a machine, and all the valves, etc., fitted in it before it is taken into the erecting shop, and therefore less time and labor will be required for attaching the different valves, cocks, etc., to the engine than must be expended when each one of the valves has to be fitted directly into the boiler shell. But besides this advantage, the steam stand possesses another one, namely, with the valve e, the steam can be at once shut off from all the valves attached to the stand, consequently, if one of these valves gets out of order, it can be repaired with full steam pressure in the boiler. The relative position of the steam stand B will greatly depend upon the position of the reverse lever ; it must be placed in a position which will bring the throttle-valve lever, as well as the reverse lever, within easy reach of the engineer ; consequently we often find that this design of throttle-valve gear is placed quite a distance in front of MODERN LOCOMOTIVE COXSTKVCTION. 369 the back head of the boiler, and differs from the position generally assigned to the throttle- valve gear in ordinary eight-wheeled passenger engines. In fact, in the latter class of engines the boiler seldom extends more than 12 to 15 inches into the cab ; hence, the steam stand illustrated in Figs. 536, 537 is not suitable for this class of engines, because there is no room for it. The short extension of the boiler into the cab, and general design of passenger engines, necessitate the use of throttle-valve gears such as have been illustrated in Figs. 514, 517, 519. When one of the latter class of throttle-valve gears has to be used, the steam-gauge stand becomes an independent fixture, and, for the sake of convenience to the engineer, it is generally fastened to the curved part of the back head of the boiler. STEAM-GAUGE STAND. 370. Fig. 544 represents a steam-gauge stand for passenger engines and for that class of engines whose boiler projects but little into the cab. This stand is arranged for a steam-gauge and clock, the latter being placed above the former. In this figure we also see an outside view of the spring balance S connected to the lever C. The rod E extends upwards and is connected to the safety-valve lever. A portion of the lever C is represented in section, so as to show the spiral spring underneath the pawl D. The spiral spring keeps the pawl engaged with the circular rack e, and prevents the lever C from being pulled upwards by the tension of the spring balance. The lever C swings on the pivot f, which is cast to the steam-gauge stand; hence, in pulling the lever C down- wards the tension of the spring will be increased, and therefore the force which presses the safety valve against the seat will also be increased. Pressing the pawl D towards the lever C disengages the pawl and rack, allowing the lever to move upwards, thus enabling the engi- neer to blow off steam when necessary. Another view of the pawl is shown at D 2 . The nuts g g fasten the steam- gauge lamp to the stand. Fig. 545 rep- resents a plan of the lever (7, and a JT w/ 5-/-A section of the steam-gauge stand. Fig. 546 represents a side view of the same steam-gauge stand. This side view is drawn to a larger scale, so as to enable us to illustrate more distinctly a section of the 370 MODERN LOCOMOTIVE CONSTRUCTION. spring balance. This spring balance consists of an outer and inner casing, a spring which connects the two, and nuts for regulating the tension of the spring. The Fig. 550 Fig. 54G __;<2 ?V 3*=-~ ^% Fig. 5.48 M L- .~ A Fig. 547 casings are made of brass tubes. The outer casing is open at the bottom, and a small brass head B is brazed in its upper end ; this head is bored out to receive the brass nut H, of which separate views are shown in Fig. 549. The inner casing is open at MODERN LOCOMOTIVE CONSTRUCTION. 371 the top, and closed at the bottom by the brass head A brazed to it. A separate view of the inner casing is shown in Fig. 547 ; a portion of the upper end of this casing is cut off for convenience in putting the spring balance together. Fig. 548 represents the spiral springs, one placed inside of the other, and fastened to the brass end-pieces L and M; a plan of the end-piece L is shown at L^ and a plan of the lower end-piece M is shown at M 2 ; in this figure the ends of the two springs are also seen. The piece L is fastened to the head of the outer casing by means of two screws, as shown at $2, Fig. 546, which is another section of the upper part of the outer casing ; the end-piece M is attached to the head at the bottom of the inner casing. The upper end of the outer casing fits in the recess of the cap 7), of which separate views are shown in Fig. 550. This cap is not fastened to the casing. The feather p, shown in Fig. 550, engages with the groove cut in the outer surface of the nut H; hence, in turning the cap, the nut must also turn, causing an increase or decrease in the tension of the spring. The nut F, Fig. 546, is simply a jam nut. Examining the section in Fig. 546, it will be seen that the head of the nut H bears against the under side of the upper end-piece L of the springs ; consequently the outer casing will not be subjected to any vertical stress due to the pressure on the safety valve ; the two small screws connecting the head of the outer casing and the end-piece L are simply for the purpose of preventing the piece L from turning, thereby keeping the springs free from any torsional strain. The tension of the springs can, of course, be regulated to a limited extent by means of the lever (7, of which other views are shown in Figs. 544, 545. The nut II and cap D are for the purpose of closer adjustment of the tension. In Fig. 546, represents the clock, G the steam-gauge, and L the lamp. SAFETY VALVE, DOME, AND CASING. 371. Fig. 551 represents a common safety valve, its attachments, and a portion of the dome top marked D. Occasionally the opening for the common safety valve in dome top is bushed with brass, but generally it is not bushed. The safety valve A is made of brass; it consists of a hollow cone with four wings, a a, cast to it, which guide the valve in the opening. Frequently the valve seat is made flat, leaving only a bearing of -fa inch all around, as shown in the illustration, but this is not the best form. The seat should have an inclination of 45 degrees to the center line of its axis, thereby obtaining an additional face-to-face metal impingement, which insures tightness under a high boiler pressure. This is an important matter, particularly for the higher pressures as are now used in locomotives, because with an increased metal impingement the valve will keep tight to a limit nearer to the blowing-off point than those with flat seats. An angle less than 45 degrees would be still better to insure against leakage, but with this comes the danger of the valve sticking to its seat. Hence, the seat beveled to an angle of 45 degrees we believe to be the best. The surface of the seat should not be conical ; it should be spherical, so that the valve will always be tight even when there is not the proper alignment of motion from tlif want of accuracy, of workmanship, or from wear. The radius of this surface is found in the following manner : Draw the valve seat as shown in Fig. 551A ; bisect 372 MODERN LOCOMOTIVE CONSTRUCTION. MODERN LOCOMOTIVE CONSTRUCTION. 373 a b and c d by perpendiculars, cutting each other in the point o; then o a will be the required radius. Two views of the safety-valve lever F are shown in Fig. 551, F 2 being the plan. The rounded end of the wrought-iron valve spindle B sets in the hollow part of the valve. The wrought-iron fulcrum C is screwed into the dome top. Another view of this fulcrum is shown at (7 2 . The rod E is a portion of the rod marked E in Fig. 546. The opening in the top of dome for this kind of safety valve is three inches in diameter for all locomotives, excepting very small ones, say with cylinders nine or ten inches in diameter ; and even for these engines the safety-valve opening is sometimes three inches in diameter. This form of safety valve is often adopted when the dome is close to the cab, as shown in Fig. 552 ; it is placed on the right-hand side of the engine, a pop being placed on the other side. When the dome is placed on the center of the boiler, the common safety valve here shown is not suitable, because its lever will be too long, and therefore a pop valve is used in its place. Some master-mechanics use the latter valve exclusively on all engines. The advantage claimed for the common safety valve with the spring balance arranged as illustrated is that it can be adjusted very conveniently without going outside of the cab to blow off at any desired steam pressure. On the other hand, the pop valve has a greater venting capacity, and is therefore sometimes preferred. These valves will be described later. 372. Fig. 552 represents a section of a portion of the boiler B and the dome D ; it shows plainly the position of the steam-gauge stand in the cab, also the manner of connecting the spring balance S, by means of the rod E, to the safety-valve lever F. The whistle lever is marked G ; details of the whistle and connections will be shown later. We also see the position of the throttle pipe in the dome, and the general arrangement of the throttle gear. The throttle lever, which is not shown, connects to the jaw 7, and the manner of opening the throttle valve, by pulling out the throttle rod //, can readily be traced. The steam-pipe T is allowed to rest on the crown bars V, being secured in posi- tion by the clamp W, which is bolted to the side of the dome. We also see the rela- tive position of the reverse lever />, which is shown in full gear forward. The reverse lever is, with veiy few exceptions, always placed on the right-hand side of the engine ; it is shown here for the sake of completeness ; had we strictly followed the rules of drawing we could not have shown the reverse lever, because that side of the engine is cut off. The section here shown is that of a switching engine with a saddle tank A A, but the relative positions of steam-gauge stand, reverse lever, and throttle lever do not differ from those in ordinary eight-wheeled passenger engines. In the latter class of engine we have, of course, no tank on the top of boiler, and therefore the dome casing extends to the top of the lagging K. The casing here shown consists of a cast-iron ring M, which, in passenger engines, is fitted to the top of the lagging, and the sheet- iron or brass casing, which is made in three parts, namely, the lower ring N, the body P, and the upper ring 0. The casing is not fastened to the dome, but is kept in place 374 MODERN LOCOMOTIVE CONSTRUCTION. by the lagging around the dome, to which it is fitted pretty closely, and can readily be lifted off when repairs to the boiler become necessary. In our illustration the boiler extends a little further into the cab than it generally does in passenger engines. In some of these engines the lagging around the boiler extends only up to the cab ; in others it extends to the back head of the boiler. TENSION ON SAFETY-VALVE SPBINGS. 373. The tension on the springs in the spring balance S (Fig. 546), the length of safety-valve lever, etc., are determined by well-known rules. Before we give these rules, let us first establish a formula from which they may be derived ; such a course will give us a clearer conception of them. In Fig. 553 the line e e 2 represents the center line of the rod marked E in Figs. 546, 551. This rod is, of course, subjected to a tensile stress due to the steam pressure on the safety valve, and this stress is transmitted to the spring balance; hence we may say that the tension on the spring is equal to the stress on the rod whose center line is rep- resented by the line e e z in Fig. 553. The weight of the safety-valve lever, weight of valve, and weight of valve spindle will, of course, help to resist the steam pressure on the valve, and will therefore re- duce the tension on the springs, and in some cases this reduction in the tension will be considerable. For the sake of simplicity we shall, in the first place, give the rules in which the weights of the safety-valve lever, valve, and valve spindle are neglected. Let L represent the distance in inches from the center of the fulcrum to the center line e e 2 ; this distance is often called the length of the safety-valve lever. B, the distance in inches from the center of the fulcrum to the center of the valve spindle. T, the tension in pounds on the springs. A, the area in square inches of the safety valve ; this area must always be taken equal to the cross-sectional area of the safety-valve opening D. P, the pressure of the steam in pounds per square inch of the safety-valve area. W 2 , the weight in pounds of the safety valve and its spindle. W 3J the weight in pounds of the safety-valve lever. C, the distance in inches from the center of fulcrum to the center of gravity G of the lever. In neglecting the weight of the safety-valve lever, valve, and spindle, the symbols Wft W 3 , and C will not be used ; we have given them here so as to make our table of symbols complete. The total steam pressure in pounds on the safety valve is evidently equal to the Fig. 5SS MODERN LOCOMOTIVE CONSTRUCTION. 375 product obtained by multiplying the steam pressure P per square inch by the area A of the valve ; hence the total pressure on the valve is equal to P x A. But this total steam pressure acts with a leverage B, and is resisted by the tension T acting with a leverage L. Now in order to compare the intensity with which the pressure on the valve acts, with the intensity with which the tension acts, we must find the moment of each of these forces. The moment of the total steam pressure acting on the valve is equal to P x A x B. The moment of the tension is equal to T x L. When the steam pressure on the valve is just sufficient to raise the valve, we have then a condition of equilibrium, in which the moment of the total steam pressure is equal to the moment of the tension, and these conditions are represented by the formula PxAxB=TxL. Putting this formula in words, we have : The product obtained by multiplying the steam pressure per square inch by the area in square inches, and by the distance from the center of the valve to the center of the fulcrum, is equal to the product obtained by multiplying the tension in pounds by distance from the line of action of the tension to the center of the fulcrum. From this formula we derive the well-known rules which will enable us to solve any problem relating to the safety valve, and these rules hold true when a weight is substituted for the springs, as in safety valve for stationary boilei's ; all we need to remember is that the center of the weight will lie in the line e e 2 . We must also bear in mind that, in the following rules, the weight of the safety-valve lever, valve, and spindle are neglected. EXAMPLE 116. The length L (Fig. 553) is 38 inches ; the distance B from the center of the valve to the center of the fulcrum is 3 J inches ; the steam pressure P per square inch is 120 pounds ; the safety valve is 3 inches diameter. What will be the tension on the springs ? The area A of a safety valve 3 inches diameter is 7.06 square inches. Here, then, we have given P, A, B, and L ; it is required to find T. We know that PxAxB=TxL; hence, to find T, we have PxAxB _ L T, (a) which reads : RULE 87. The steam pressure in pounds per square inch, multiplied by the area in square inches of the safety valve, and this product again multiplied by the distance in inches from the center of the valve to the center of the fulcrum, and the last prod- uct divided by the length of the lever in inches, will give the tension in pounds of the springs. Substituting the numerical values for the symbols in formula (a), we have 120 x 7.06 x 3.5 ,, s - - = <7 pounds for the tension of the springs. EXAMPLE 117. The tension T is 77 pounds; the distance B (Fig. 553) is 3 inches; 376 MODERN LOCOMOTIVE CONSTRUCTION. the area A of the valve, 7.06 square inches ; steam pressure P, 120 pounds per square inch. Find the length L of the safety-valve lever. Here we have P x A x B -jr- - = L, (I) which reads : RULE 88. The steam pressure in pounds per square inch, multiplied by the area in square inches of the safety valve, and this product again multiplied by the distance from the center of the valve to the center of the fulcrum, and the last product divided by the tension in pounds, will give a quotient which is numerically equal to the length of the lever in inches. Substituting the numerical values for the symbols in formula (6), we have 120 x 7.06 x 3.5 ^ - = 38.5 inches for the length of the safety-valve lever. EXAMPLE 118. The tension T is 77 pounds ; length L of the safety-valve lever, 38 J inches; area A of the valve, 7.06 square inches; distance B from the center of the valve to the center of the fulcrum, 3j inches. Find the steam pressure per square inch on the safety valve. Here we have T x L A x B = ' ^ which reads : RULE 89. The product obtained by multiplying the tension in pounds by the length of the lever in inches, divided by the product obtained by multiplying the area in square inches of the valve by the distance in inches from the center of the valve to the center of the fulcrum, will give a quotient which is numerically equal to the steam pressure per square inch. Substituting the numerical values for the symbols in fonnula (c), we have 77 x 38.5 7.06 x 3.5 = 119 ' 97 P unds steam pressure per square inch of the safety valve. EXAMPLE 119. The tension T is 77 pounds ; length of lever, 38 inches ; steam pressure, 120 pounds ; distance from the center of the valve to the center of fulcrum, 3 inches. Find the area of the valve. Here we have which reads : RULE 90. The product obtained by multiplying the tension in pounds by the length of the safety-valve lever in inches, divided by the product obtained by multi- plying the steam pressure per square inch by the distance from the center of the valve to the center of the fulcrum in inches, will give a quotient which is numerically equal to the number of square inches in the area of the safety valve. Substituting the numerical values for the symbols in formula (d), we have 77 x 38.5 i on v -3 r = 7.0o square inches -L-jU X o.O in the area of the valve. MODERN LOCOMOTIVE CONSTRUCTION. 377 EXAMPLE 120. The tension T is 77 pounds ; length of lever L, 38J inches ; steam pressure ]\ 1'20 pounds ; area A, 7.06 square inches. Find the distance from the center of the valve to the center of the fulcrum. Here wehave T*L P*A- B > which reads : RULE 91. The product obtained by multiplying the tension in pounds by the length of the lever in inches, divided by the product obtained by multiplying the steam pressure per square inch by the area in square inches of the valve, will give a quotient which is numerically equal to the distance in inches from the center of the valve to the center of the fulcrum. Substituting the numerical values for the symbols in formula (c), we have 77 x 38.5 120 x 7.06 = 3 ' 49 mches ' which is the distance from the center of the valve to the center of the fulcrum. When the weight of the safety-valve, lever, etc., are taken into account, the formulas become a little more complicated ; but if the foregoing formulas and rules are understood, there will not be any difficulty in forming a clear conception of the rules in the next article. 374. In the following rules relating to safety-valve problems, the weight of the valve, lever, and spindle is to be taken into account. These weights must be accu- rately ascertained, either by actual weighing or by computation. The weight of the safety-valve lever will act on the valve with a leverage which is equal to the distance from the center of gravity of the lever to the fulcrum. In other words, we assume that the whole weight of the safety-valve lever is concentrated at its center of gravity G (Fig. 553), and acts with a leverage C. When the safety-valve lever is of uniform thickness and width throughout, and the shape of one end exactly like that of the opposite end, we may, for all practical purposes, assume the center of gravity to lie in the center of the lever, and, indeed, it will be there exactly, provided no holes are drilled through the lever, and the metal is homogeneous. When the lever is not of uniform thickness throughout, then, in order to find the center of gravity, the lever should be balanced on a knife-edge, and when in equilib- rium, the center of gravity will lie in a vertical line drawn across the lever from the knife-edge. When the lever is of uniform thickness throughout, but not of uniform width, we may also find the center of gravity by balancing the lever on a knife-edge. This method may not always be convenient; in such cases we may adopt the following method, which will give us an approximate position of the center of gravity ; but it should be distinctly understood that this method is only applicable to levers which have a uniform thickness. Nearly all safety-valve levers for locomotives are of uniform thickness, with the exception of the small hub around the center line < c.^ in Fig. 553. To allow for this hub, assume the lower edge of the lever to extend 378 MODERN LOCOMOTIVE CONSTRUCTION. lot clear to its end and proceed as follows: Cut a template out of stiff paper, con- forming to the width of the lever. Anywhere near one of the edges of this template punch a small hole, for instance at A (Fig. 553a), and suspend the template from a pin passed through this hole, allowing the template to have plenty of freedom to vibrate ; also, from the same pin suspend a plummet-line, and along it draw a pencil line A B on the template. In a similar way suspend the template from another hole C, punched anywhere near the edge opposite the hole A ; along the plummet-line draw on the template another pen- cil line C D, cutting A B in the point G, which will be the position of the center of gravity. The preliminary details having been arranged, we are in a position to establish a formula, from which all subsequent rules relating to the safety-valve can be deduced. Since these rules will be interesting examples of the principle of mo- ments, it may be advantageous to repeat the definition of the moment of a force given in Art. 256. The moment of a force with respect to a point is the product obtained by multiplying the force by the perpendicular distance from the point to the direction of the force. Now the point referred to in this definition is the center of the ful- crum-pin in Fig. 553. About this point there are four forces acting namely, the steam pressure acting in the direction of the vertical line through the center of the valve; the total steam pressure is evidently equal to P x A (here the same symbols are used as given in Art. 373), hence, according to our definition, the moment of this pressure about the fulcrum is equal to P x A x B. Second, the tension acting in the direction of the vertical line e e 2j hence its moment about the fulcrum is equal to T x L. Third, the weight W 2 of the valve and spindle acting in a direction of the vertical line through the center of the valve, hence its moment about the fulcrum is equal to W 2 x B. And lastly, the weight W~ 3 of the lever, acting in a vertical line through the center of gravity G, hence its moment about the fulcrum is equal to W 3 x C. The moment P x A x B acts upwards, all the other moments act downwards ; and when the steam pfessure is just sufficient to raise the valve, we have then a condition in which the upward moment is equal to the sum of the downward moments. Sum- ming up the downward moments, we have : Moment of the tension T about the fulcrum = T x L. Moment of the weight W z about the fulcrum = TF 2 x B. Moment of the weight W 3 about the fulcrum = W 3 x C. Sum of the downward moments = (T x L) + (W 2 x B) + (TF-, x C). Since the sum of these moments must be equal to the upward moment, we have : P x A x B = (T x L) + (W 2 x B) + (W 3 x C). (/) B Fig. 5S3a From this formula all rules relating to the safety valve can be deduced. EXAMPLE 121. Tension of the springs T= 72.27 pounds. MODERN LOCOMOTIVE CONSTRUCTION 379 Length L of lever = 38.5 inches. Weight W 3 of lever = 11 pounds. Distance C of center of gravity of lever from the fulcrum = 15 inches. Weight W 2 of valve and spindle = 5 pounds. Distance B from center of valve to fulcrum = 3.5 inches. Area A of the valve = 7.0G square inches. Find the steam pressure P per square inch. Here we are to find P ; hence from formula (b) we obtain , 2 , ~A^B~ which reads : RULE 92. Add the moment of the tension, the moment of weight of the valve and spindle, and the moment of weight of the lever; divide this sum by the product obtained by multiplying the area of the valve by the distance from the fulcrum to the center of the valve ; the quotient will be the steam pressure per square inch on the valve. In this and the following rules, all the dimensions should be taken in inches, and the weights in pounds. Substituting the numerical values for the symbols in formula (g), we have (72.27 x 38.5) + (5 x 3.5) + (11 x 15) P = L -- 7.06X3* - ' = 119 ' 9+ POUndS ' EXAMPLE 122. The steam pressure per square inch is 120 pounds ; the weights and dimensions of the safety valve are as given in Example 121, with the exception of the area of the valve, which is to be found. Here we have , 3 .,. PxB which reads : RULE 93. Add the moment of the tension, the moment of the weight of valve and spindle, and the moment of the lever ; divide this sum by the product obtained by multiplying the steam pressure per square inch by the distance from the fulcrum to the center of the valve ; the quotient will be the area of the valve in square inches. Substituting the numerical values for the symbols in formula (/*), we obtain (72.27 x 38.5) + (5 x 3.5) + (11 x 15) 1 9Q x S 5 = square inches. EXAMPLE 123. The steam pressure is 120 pounds, the weights and dimensions of the safety valve are as given in Example 121, with the exception of the distance from the fulcrum to the valve, which is to be found. Here we are to find B, hence G) 2 3 AxP which reads : RULE 94. Add the moment of the tension, the moment of the weight of the valve and spindle, and the moment of the weight of the lever; divide this sum by the 380 MODERN LOCOMOTIVE CONSTRUCTION. product obtained by multiplying the area of the valve by the steam pressure ; the quotient will be the distance from the fulcrum to the center of the valve in inches. Substituting the numerical values for the symbols in formula (i), we obtain _ (72.27 x 38.5) 4- (5 x 3.5) + (11 x 15) 7.06 x 120~ = 3 ' 49 inches< In order to find the tension we must change our original formula (/) to the following : (P x A x B) - (W 2 x B) - (W 3 x C) = T x L. (j) From this we obtain _ (P*AxB)-(W 2 xB)-(W 3 x C) , M ~L~ which reads : RULE 95. From the moment of the steam pressure subtract the moment of the weight of valve and spindle, also subtract the moment of the lever; divide the remainder by the length of the lever ; the quotient will be the tension in pounds. EXAMPLE 124. The steam pressure is 120 pounds per square inch; all other dimensions are as given in Example 121, excepting the tension, which is to be found. Substituting the numerical values for the symbols in formula (k), we have (120 x 7.06 x 3.5) - (5 x 3.5) - (11 x 15) 1 '- og - = 72.27 pounds. For finding the length L of the safety-valve lever when all other dimensions and weights are given, we have the following formula : (P x A x B) - (W 2 x B) - (W 3 x C) A L = - ~~T~ ~' In this formula we have taken into account W 3 , which is the weight of the lever, and C, which is the distance from the fulcrum to the center of gravity of the lever, and, since these cannot be accurately determined unless the length L of the lever is known, we are compelled to assume a value for W 3 x C. Probably under these circumstances it will be best to find the length L of the lever by formula (6), Art. 373 ; the length L thus found will be somewhat longer than that obtained by formula (I). DOME TOPS. 375. The safety valves are generally attached to a cast-iron dome top, the propor- tions of which are shown in Figs. 554, 555 ; the relative positions of the safety valves and the whistle are also given. The safety valve, such as is shown in Fig. 553, is placed in the opening A, and the locked safety valve, or pop valve, is placed in the opening B. The whistle is screwed into the central hub E, and stands forward of the safety valves. When the ordinary plain safety valve is used, we do not require the hubs f, f, shown in Fig. 555 ; yet these are generally cast to the dome top so that any other safety valve can readily be attached. The basin C is simply for the purpose of MODERN LOCOMOTIVE CONSTRUCTION. 381 collecting the water due to the condensation of steam as i